GRE Quantitative Flashcards: Area Perimeter Volume

What this deck covers

This deck focuses on Area Perimeter Volume, giving you a quick way to review the definitions, rules, and examples that matter most for GRE Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the volume formula for a right circular cone with radius $r$ and height $h$?

Answer: $V=\frac{1}{3}\pi r^2h$. Takes one-third of the cylinder's volume with the same base and height due to the cone's tapering shape.

Flashcard 2: What is the volume formula for a right circular cylinder with radius $r$ and height $h$?

Answer: $V=\pi r^2h$. Multiplies the circular base area by the height to find the cylinder's volume.

Flashcard 3: What is the area formula for a rhombus (or kite) with diagonals $d_1$ and $d_2$?

Answer: $A=\frac{1}{2}d_1d_2$. Uses half the product of the diagonals, as they bisect the rhombus or kite into four right triangles.

Flashcard 4: What is the area of a square with side length $s$?

Answer: $A=s^2$. Squares the side length to compute the area enclosed by the square.

Flashcard 5: What is the area formula for a circle with radius $r$?

Answer: $A=\pi r^2$. Calculates the space inside the circle using pi times the square of the radius.

Flashcard 6: What is the area formula for a triangle with base $b$ and height $h$?

Answer: $A=\frac{1}{2}bh$. Takes half the product of base and height since the area is half of a parallelogram with the same base and height.

Flashcard 7: Identify the scale factor for area if all linear dimensions are multiplied by $k$.

Answer: Area is multiplied by $k^2$. Scales with the square of linear dimensions, multiplying area by $k^2$.

Flashcard 8: What is the surface area formula for a rectangular solid with dimensions $l,w,h$?

Answer: $SA=2(lw+lh+wh)$. Sums the areas of all six faces by doubling the products of each pair of dimensions.

Flashcard 9: What is the volume formula for a pyramid in terms of base area $B$ and height $h$?

Answer: $V=\frac{1}{3}Bh$. Uses one-third of the prism's volume with the same base and height due to the pyramid's apex convergence.

Flashcard 10: What is the volume formula for a sphere with radius $r$?

Answer: $V=\frac{4}{3}\pi r^3$. Derives from integrating cross-sectional areas, resulting in four-thirds pi times radius cubed.

Flashcard 11: What is the perimeter formula for a rectangle with length $l$ and width $w$?

Answer: $P=2l+2w$. Adds twice the length and twice the width to account for opposite sides of the rectangle.

Flashcard 12: What is the area of a rectangle with $l=7$ and $w=3$?

Answer: $A=21$. Applies the rectangle area formula by multiplying length 7 by width 3.

Flashcard 13: What is the volume of a cylinder with radius $r=2$ and height $h=5$?

Answer: $V=20\pi$. Computes using the cylinder volume formula with base area $\pi (2)^2$ times height 5.

Flashcard 14: What is the perimeter of a square with side length $s$?

Answer: $P=4s$. Multiplies the side length by four since all sides of the square are equal.

Flashcard 15: What is the surface area formula for a sphere with radius $r$?

Answer: $SA=4\pi r^2$. Represents the total surface as four times the area of a great circle of the sphere.

Flashcard 16: What is the circumference formula for a circle with radius $r$?

Answer: $C=2\pi r$. Represents the total length around the circle as twice pi times the radius.

Flashcard 17: Identify the scale factor for perimeter if all linear dimensions are multiplied by $k$.

Answer: Perimeter is multiplied by $k$. Scales linearly with the dimensions, so perimeter increases by the factor $k$.

Flashcard 18: What is the volume formula for a rectangular solid with dimensions $l,w,h$?

Answer: $V=lwh$. Multiplies the three dimensions to determine the space occupied by the rectangular solid.

Flashcard 19: What is the area formula for a trapezoid with bases $b_1,b_2$ and height $h$?

Answer: $A=\frac{1}{2}(b_1+b_2)h$. Averages the two bases and multiplies by height to account for the trapezoid's shape.

Flashcard 20: What is the volume formula for a prism in terms of base area $B$ and height $h$?

Answer: $V=Bh$. Multiplies the base area by the height to fill the prism's cross-sectional shape along its length.

Flashcard 21: What is the area formula for a parallelogram with base $b$ and height $h$?

Answer: $A=bh$. Multiplies base by perpendicular height to find the enclosed area, regardless of side angles.

Flashcard 22: What is the area of a semicircle with radius $r$ (excluding the diameter as boundary detail)?

Answer: $A=\frac{1}{2}\pi r^2$. Halves the full circle's area since a semicircle covers half the space without including the diameter's contribution.

Flashcard 23: Identify the scale factor for volume if all linear dimensions are multiplied by $k$.

Answer: Volume is multiplied by $k^3$. Scales with the cube of linear dimensions, multiplying volume by $k^3$.

Flashcard 24: What is the area formula for a rectangle with length $l$ and width $w$?

Answer: $A=lw$. Multiplies length by width to calculate the total space enclosed by the rectangle.

Flashcard 25: What is the total surface area formula for a right circular cylinder with radius $r$ and height $h$?

Answer: $SA=2\pi r^2+2\pi rh$. Adds the areas of two bases and the lateral surface, which unwraps to a rectangle of width $2\pi r$ and height $h$.