7th Grade Math Quiz: Describe Cross Sections Of 3d Figures

What this quiz covers

This quiz focuses on Describe Cross Sections Of 3d Figures, giving you a quick way to practice the rules, question types, and explanations that matter most for 7th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Triangle
2. Pentagon
3. Circle
4. Rectangle (correct answer)

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular prism sliced horizontally (parallel to base) gives rectangle cross-section (cuts through vertical faces creating rectangular outline), sliced vertically gives rectangle (through opposite faces). For example, a rectangular prism sliced vertically perpendicular to the base shows a rectangle cross-section (sides matching the height and width of the faces it cuts). The correct cross-section identification is a rectangle, as the vertical slice cuts through the height and two opposite faces, forming a rectangular shape. A common error is claiming it's a circle (wrong, rectangle—prisms have rectangular faces, not circular). To determine the cross-section: (1) identify the 3D figure (rectangular prism), (2) identify slice orientation (vertical=perpendicular to base), (3) apply rules (vertical through faces→rectangle for prism), (4) name 2D shape (rectangle). Key patterns: prism horizontal/vertical both rectangles (rectangular faces), but common mistakes include confusing with pyramids where vertical slices give triangles.

Question 2

1. 16 square units, because the area decreases by the height ratio
2. 24 square units, because the area decreases linearly with height
3. 9 square units, because the area scales with the square of linear dimensions (correct answer)
4. 12 square units, because the area decreases by half the height difference

Explanation: Cross-sections parallel to the base are similar squares. At 1/3 height from base (2/3 from apex), linear scale factor is 2/3. At 2/3 height from base (1/3 from apex), linear scale factor is 1/3. Since the lower section has area 36 and scale factor 2/3, the base area is 36 ÷ (2/3)² = 81. The upper section area is 81 × (1/3)² = 9 square units.

Question 3

1. 2.5 units, because the pyramid shrinks uniformly toward the apex (correct answer)
2. 7.5 units, because three-fourths of the original length remains
3. 4.0 units, because the height ratio creates proportional scaling
4. 6.25 units, because the area decreases by the height ratio

Explanation: In a right rectangular pyramid, horizontal cross-sections are similar to the base with a scaling factor based on distance from the apex. At 3/4 up from base means 1/4 down from apex. The side length scales proportionally: remaining fraction × original side = 1/4 × 10 = 2.5 units.

Question 4

1. 3 sides, forming an equilateral triangle with all angles equal (correct answer)
2. 4 sides, forming a quadrilateral with two pairs of equal sides
3. 3 sides, forming an isosceles triangle with two equal sides only
4. 6 sides, forming a hexagon with alternating side lengths

Explanation: When a plane passes through the midpoints of three edges meeting at a vertex of a cube, it intersects exactly three faces, creating a triangle. Since all edges of a cube are equal and the cutting points are all midpoints, the resulting triangle is equilateral with all sides equal and all angles 60°.

Question 5

1. Triangle (correct answer)
2. Parallelogram
3. Rectangle
4. Circle

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular pyramid sliced horizontally gives smaller rectangle (parallel to base, similar shape decreasing toward apex), sliced vertically through apex gives triangle (apex is vertex, base edge is side, isosceles if through center). For example, a rectangular pyramid sliced vertically through the apex shows a triangle cross-section (three vertices: apex and two base corners). The correct cross-section identification is a triangle, as the plane passes through the apex point and cuts the base edge, forming three sides. A common error is claiming it's a rectangle (wrong, triangle—vertical through apex creates a pointed shape, not rectangular). To determine the cross-section: (1) identify the 3D figure (rectangular pyramid), (2) identify slice orientation (vertical through apex), (3) apply rules (through apex→triangle), (4) name 2D shape (triangle). Key patterns: pyramid horizontal rectangle but vertical triangle (apex creates point), and orientation matters—horizontal vs vertical differ significantly.

Question 6

1. Rectangle (correct answer)
2. Ellipse
3. Circle
4. Pentagon

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: cylinder horizontal gives circle (parallel to circular base maintains circular shape), vertical through axis gives rectangle. For example, a cylinder sliced vertically through the axis shows a rectangle cross-section (height as sides, diameter as width). The correct cross-section identification is a rectangle, as the plane cuts along the height and through the curved surface, unfolding to straight lines. A common error is claiming it's a circle (wrong, rectangle—vertical through axis, circle for horizontal). To determine the cross-section: (1) identify the 3D figure (cylinder), (2) identify slice orientation (vertical through axis), (3) apply rules (vertical through axis→rectangle), (4) name 2D shape (rectangle). Key patterns: cylinder horizontal circle but vertical rectangle, and common mistakes include confusing with ellipses (which occur for slanted slices).

Question 7

1. Rectangle
2. Circle (correct answer)
3. Triangle
4. Trapezoid

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: cylinder horizontal gives circle (parallel to circular base maintains circular shape), vertical through axis gives rectangle. For example, a cylinder sliced horizontally shows a circular cross-section (parallel to the circular base, maintaining the round shape). The correct cross-section is a circle, as the horizontal slice parallel to the base of a cylinder follows the base's shape. A common error is choosing rectangle (wrong, as that's for vertical slices through the axis; horizontal in cylinders yields circles, not rectangles). To determine the cross-section: (1) identify the 3D figure as a cylinder, (2) note the slice is horizontal and parallel to the base, (3) apply the rule that parallel to the base gives the same shape as the base (circle), (4) name the 2D shape as circle. Key patterns include cylinders and cones producing circles for horizontal slices due to their circular bases, unlike prisms with rectangular ones, with mistakes confusing orientation and claiming rectangles from horizontal cuts.

Question 8

1. Trapezoid
2. Triangle
3. Rectangle (correct answer)
4. Circle

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular prism sliced horizontally (parallel to base) gives rectangle cross-section (cuts through vertical faces creating rectangular outline), sliced vertically gives rectangle (through opposite faces). For example, a rectangular prism like a cereal box sliced horizontally parallel to the base shows a rectangle cross-section (top and bottom edges parallel, sides straight—rectangular outline). The correct cross-section identification is a rectangle, as the horizontal slice parallel to the base mirrors the rectangular base shape. A common error is thinking a horizontal prism slice gives a triangle (wrong, it's a rectangle—prism faces are rectangles, horizontal cuts parallel giving rectangle). To determine the cross-section: (1) identify the 3D figure (rectangular prism), (2) identify slice orientation (horizontal=parallel to base), (3) apply rules (parallel to base→same shape as base for prism), (4) name 2D shape (rectangle). Key patterns: prism horizontal/vertical both rectangles (rectangular faces), and orientation matters—horizontal vs vertical can differ in other shapes like pyramids.

Question 9

1. A horizontal slice parallel to the base of a cylinder
2. A vertical slice through the apex of a rectangular pyramid (correct answer)
3. A horizontal slice parallel to the base of a rectangular prism
4. A horizontal slice parallel to the base of a cone

Explanation: Tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular prism sliced horizontally (parallel to base) gives rectangle cross-section (cuts through vertical faces creating rectangular outline), sliced vertically gives rectangle (through opposite faces). Rectangular pyramid sliced horizontally gives smaller rectangle (parallel to base, similar shape decreasing toward apex), sliced vertically through apex gives triangle (apex is vertex, base edge is side, isosceles if through center). For example, rectangular pyramid vertical through apex showing triangle (three vertices: apex and two base corners), or rectangular prism sliced horizontally showing rectangle cross-section (top and bottom edges parallel, sides straight—rectangular outline), or cylinder horizontal showing circular cross-section (parallel to circular base). The correct identification for producing a triangle is a vertical slice through the apex of a rectangular pyramid, as it cuts from the point to the base, forming three sides. A common error is choosing horizontal slice of a prism (wrong, rectangle—not tapering to point), or horizontal cone (wrong, circle—parallel to base). Determining cross-section: (1) identify 3D figure (prism, pyramid, cylinder, cone), (2) identify slice orientation (horizontal=parallel to base, vertical=perpendicular to base, through specific features like apex/axis), (3) apply rules (parallel to base→same shape as base for prism, smaller for pyramid/cone; through apex→triangle; vertical through cylinder axis→rectangle), (4) name 2D shape (rectangle, triangle, circle, etc.). Key patterns: prism horizontal/vertical both rectangles (rectangular faces), pyramid horizontal rectangle but vertical triangle (apex creates point), cylinder/cone horizontal circles (circular bases), vertical through axis rectangles or triangles (cone apex).

Question 10

1. Circle (correct answer)
2. Triangle
3. Rectangle
4. Square

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: cone horizontal gives circle (smaller toward apex), vertical through apex gives isosceles triangle. For example, a cone sliced horizontally shows a circular cross-section (parallel to the base but smaller due to tapering). The correct cross-section is a circle, as the horizontal slice parallel to the base of a cone follows the base's round shape, just reduced. A common error is choosing triangle (wrong, as that's for vertical slices through the apex; horizontal in cones yields circles, not triangles). To determine the cross-section: (1) identify the 3D figure as a cone, (2) note the slice is horizontal and parallel to the base, (3) apply the rule that parallel to the base gives a smaller circle, (4) name the 2D shape as circle. Key patterns include cones producing smaller circles for horizontal slices due to tapering, similar to pyramids but with round bases, with mistakes confusing cones with prisms and claiming rectangles.

Question 11

1. Triangle (correct answer)
2. Square
3. Circle
4. Rectangle

Explanation: When a cone is sliced by a vertical plane that passes through both the apex and the center of the circular base, the cut goes from the single point at the top down to a straight line across the base, creating a shape with three straight sides, which is a triangle, matching choice A. Choice C, a circle, would only result from a horizontal slice parallel to the base, not a vertical slice through the apex. Choice D, a rectangle, would only happen with shapes that have parallel flat sides all the way up, like a cylinder or prism, which a cone does not have. Choice B, a square, does not match any standard cross-section of a cone at all. The key idea is that any vertical slice through a cone's apex tapers to a single point, which always produces a triangular cross-section.

Question 12

1. Rectangle
2. Triangle (correct answer)
3. Circle
4. Trapezoid

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: cone horizontal gives circle (smaller toward apex), vertical through apex gives isosceles triangle. For example, a cone sliced vertically through the apex shows a triangle cross-section (apex as vertex, base diameter as base side). The correct cross-section identification is a triangle, as the plane passes through the tip and cuts the base, forming three sides. A common error is claiming it's a circle (wrong, triangle—vertical through apex, circle for horizontal). To determine the cross-section: (1) identify the 3D figure (cone), (2) identify slice orientation (vertical through apex), (3) apply rules (through apex→triangle), (4) name 2D shape (triangle). Key patterns: cone horizontal circle but vertical triangle (apex creates point), and orientation matters—horizontal vs vertical differ like in pyramids.

Question 13

1. Triangle
2. Rectangle
3. Circle (correct answer)
4. Trapezoid

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: cylinder horizontal gives circle (parallel to circular base maintains circular shape), vertical through axis gives rectangle. For example, a cylinder like a soup can sliced horizontally parallel to the base shows a circular cross-section (matching the base shape). The correct cross-section identification is a circle, as the horizontal slice parallel to the circular base preserves the round outline. A common error is thinking it's a rectangle (wrong, circle—parallel to circular base, rectangle for vertical slices). To determine the cross-section: (1) identify the 3D figure (cylinder), (2) identify slice orientation (horizontal=parallel to base), (3) apply rules (parallel to base→circle for cylinder), (4) name 2D shape (circle). Key patterns: cylinder/cone horizontal circles (circular bases), but vertical through axis rectangles or triangles (cone apex).

Question 14

1. Rectangle (correct answer)
2. Triangle
3. Circle
4. Trapezoid

Explanation: Tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular prism sliced horizontally (parallel to base) gives rectangle cross-section (cuts through vertical faces creating rectangular outline), sliced vertically gives rectangle (through opposite faces). Rectangular pyramid sliced horizontally gives smaller rectangle (parallel to base, similar shape decreasing toward apex), sliced vertically through apex gives triangle (apex is vertex, base edge is side, isosceles if through center). For example, rectangular prism sliced horizontally showing rectangle cross-section (top and bottom edges parallel, sides straight—rectangular outline), or rectangular pyramid vertical through apex showing triangle (three vertices: apex and two base corners), or cylinder horizontal showing circular cross-section (parallel to circular base). The correct cross-section identification for a rectangular prism sliced horizontally parallel to the base is a rectangle, as the slice cuts evenly through the vertical faces, producing a shape identical to the base. A common error is thinking a horizontal prism slice gives a triangle (wrong, rectangle—prism faces are rectangles, horizontal cuts parallel giving rectangle), or confusing it with a pyramid slice. Determining cross-section: (1) identify 3D figure (prism, pyramid, cylinder, cone), (2) identify slice orientation (horizontal=parallel to base, vertical=perpendicular to base, through specific features like apex/axis), (3) apply rules (parallel to base→same shape as base for prism, smaller for pyramid/cone; through apex→triangle; vertical through cylinder axis→rectangle), (4) name 2D shape (rectangle, triangle, circle, etc.). Key patterns: prism horizontal/vertical both rectangles (rectangular faces), pyramid horizontal rectangle but vertical triangle (apex creates point), cylinder/cone horizontal circles (circular bases), vertical through axis rectangles or triangles (cone apex).

Question 15

1. Circle
2. Trapezoid
3. Triangle (correct answer)
4. Rectangle

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: cone horizontal gives circle (smaller toward apex), vertical through apex gives isosceles triangle. For example, a cone sliced vertically through the apex and base center shows a triangular cross-section (apex point and base diameter forming sides). The correct cross-section is a triangle, as the vertical slice through the apex of a cone cuts to form three sides, often isosceles. A common error is choosing rectangle (wrong, as that's for cylinder vertical slices; cones taper to a point, creating a triangle). To determine the cross-section: (1) identify the 3D figure as a cone, (2) note the slice is vertical, passing through the apex and base center, (3) apply the rule that vertical through the apex gives a triangle, (4) name the 2D shape as triangle. Key patterns include cones yielding triangles for vertical apex slices due to the point, unlike cylinders' rectangles, with mistakes from not accounting for the apex's tapering effect.

Question 16

1. Rectangle (correct answer)
2. Triangle
3. Ellipse
4. Circle

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular prism sliced horizontally (parallel to base) gives rectangle cross-section (cuts through vertical faces creating rectangular outline), sliced vertically gives rectangle (through opposite faces). For example, a rectangular prism sliced vertically from front to back shows a rectangle cross-section (height and length forming the outline). The correct cross-section is a rectangle, as the vertical slice perpendicular to the base in a rectangular prism produces a rectangular shape. A common error is choosing circle (wrong, as prisms have no curved surfaces; circles come from cylinders or cones). To determine the cross-section: (1) identify the 3D figure as a rectangular prism, (2) note the slice is vertical, perpendicular to the base and straight through, (3) apply the rule that vertical slices in prisms give rectangles, (4) name the 2D shape as rectangle. Key patterns include prisms always giving rectangles for horizontal or vertical slices due to straight faces, with mistakes claiming impossible shapes like circles from non-cylindrical figures.

Question 17

1. Trapezoid
2. Circle
3. Triangle
4. Rectangle (correct answer)

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular prism sliced horizontally (parallel to base) gives rectangle cross-section (cuts through vertical faces creating rectangular outline), sliced vertically gives rectangle (through opposite faces). For example, a rectangular prism sliced horizontally shows a rectangle cross-section (top and bottom edges parallel, sides straight—rectangular outline). The correct cross-section is a rectangle, as the horizontal slice parallel to the base of a rectangular prism produces a shape identical to the base. A common error is choosing triangle (wrong, as that's for vertical slices through a pyramid's apex, not a prism where sides are parallel and don't taper). To determine the cross-section: (1) identify the 3D figure as a rectangular prism, (2) note the slice is horizontal and parallel to the base, (3) apply the rule that parallel to the base in a prism gives the same shape as the base (rectangle), (4) name the 2D shape as rectangle. Key patterns include prisms yielding rectangles for both horizontal and vertical slices due to their uniform rectangular faces, unlike pyramids where horizontal slices are rectangles but vertical through the apex are triangles.

Question 18

1. A vertical slice that passes through the apex (correct answer)
2. A horizontal slice that passes through the base
3. A horizontal slice parallel to the base
4. A slice parallel to a side face but not through the apex

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular pyramid sliced horizontally gives smaller rectangle (parallel to base, similar shape decreasing toward apex), sliced vertically through apex gives triangle (apex is vertex, base edge is side, isosceles if through center). For example, a rectangular pyramid sliced vertically through the apex shows a triangle cross-section (three vertices: apex and two base points). The correct slice to produce a triangle is a vertical one passing through the apex, as it includes the point and base edge to form three sides. A common error is choosing horizontal parallel to the base (wrong, as that gives rectangles; triangles require the apex in the slice). To determine the cross-section: (1) identify the 3D figure as a rectangular pyramid, (2) evaluate each slice orientation, (3) apply rules like through apex for triangle versus parallel to base for rectangle, (4) select the vertical apex slice. Key patterns include pyramids needing apex inclusion for triangles, unlike prisms, with mistakes assuming horizontal slices taper to triangles instead of smaller rectangles.

Question 19

1. Circle
2. Rectangle
3. Triangle (correct answer)
4. Parallelogram

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular pyramid sliced horizontally gives smaller rectangle (parallel to base, similar shape decreasing toward apex), sliced vertically through apex gives triangle (apex is vertex, base edge is side, isosceles if through center). For example, a rectangular pyramid sliced vertically through the apex and base midpoint shows a triangle cross-section (three vertices: apex and two points on the base edge). The correct cross-section is a triangle, as the vertical slice through the apex of a rectangular pyramid cuts to form three sides. A common error is choosing rectangle (wrong, as that's for horizontal slices; vertical through the apex includes the pointy top, creating a triangle, not a rectangle). To determine the cross-section: (1) identify the 3D figure as a rectangular pyramid, (2) note the slice is vertical, passing through the apex and base midpoint, (3) apply the rule that vertical through the apex gives a triangle, (4) name the 2D shape as triangle. Key patterns include pyramids yielding triangles for vertical apex slices due to the apex point, unlike prisms where vertical slices are rectangles, with mistakes often from not considering the apex's role in forming a vertex.

Question 20

1. It is a rectangle similar to the base, but smaller. (correct answer)
2. It is a rectangle the same size as the base.
3. It is a circle because the slice is flat.
4. It is a triangle because pyramids have triangular faces.

Explanation: This question tests describing 2D cross-sections from slicing 3D figures: horizontal slices of prisms/pyramids (rectangles), vertical slices through apex (triangles), horizontal slices of cylinders/cones (circles), based on slice orientation. Cross-section shape depends on slice orientation and 3D figure: rectangular pyramid sliced horizontally gives smaller rectangle (parallel to base, similar shape decreasing toward apex), sliced vertically through apex gives triangle (apex is vertex, base edge is side, isosceles if through center). For example, a rectangular pyramid sliced parallel to the base shows a rectangle cross-section similar to the base but smaller (due to the tapering sides). The correct statement is that it is a rectangle similar to the base, but smaller, as horizontal slices produce scaled-down versions of the base shape. A common error is saying it's a triangle because pyramids have triangular faces (wrong, rectangle—parallel slice matches base shape, not faces). To determine the cross-section: (1) identify the 3D figure (rectangular pyramid), (2) identify slice orientation (parallel to base), (3) apply rules (parallel to base→smaller similar rectangle), (4) name 2D shape (rectangle). Key patterns: pyramid tapers so horizontal slices shrink, unlike prisms; common mistakes include assuming same size or confusing with vertical slices.