ISEE Upper Level Quantitative Reasoning Flashcards: Area Perimeter And Volume

What this deck covers

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

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: State the formula for the surface area of a rectangular prism with length $l$, width $w$, height $h$.

Answer: $SA=2(lw+lh+wh)$. Adds twice the areas of each pair of opposite faces to compute total surface area.

Flashcard 2: State the formula for the surface area of a cylinder with radius $r$ and height $h$.

Answer: $SA=2\pi r^2+2\pi rh$. Sums the areas of two bases and the lateral surface to find total surface area.

Flashcard 3: State the formula for the area of a rectangle with length $l$ and width $w$.

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

Flashcard 4: State the formula for the area of a circle with radius $r$.

Answer: $A=\pi r^2$. Squares the radius and multiplies by $\pi$ to compute the circle's enclosed area.

Flashcard 5: State the formula for the perimeter of a rectangle with length $l$ and width $w$.

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

Flashcard 6: State the formula for the area of a sector with radius $r$ and central angle $\theta$ degrees.

Answer: $A=\frac{\theta}{360}\pi r^2$. Takes the fraction of the full circle's area based on the central angle in degrees.

Flashcard 7: A rectangle has area $48$ and width $6$. What is its length?

Answer: $8$. Divides the area by the width to solve for length using $A=lw$.

Flashcard 8: State the formula for the volume of a rectangular prism with length $l$, width $w$, height $h$.

Answer: $V=lwh$. Multiplies length, width, and height to find the space occupied by the rectangular prism.

Flashcard 9: Find the volume of a cylinder with $r=2$ and $h=9$ in terms of $\pi$.

Answer: $36\pi$. Multiplies base area $\pi r^2$ by height for the cylinder volume.

Flashcard 10: Find the area of a triangle with base $b=10$ and height $h=6$.

Answer: $30$. Uses the triangle area formula $A=\frac{1}{2}bh$ with the provided base and height.

Flashcard 11: State the formula for the area of a triangle with base $b$ and height $h$.

Answer: $A=\frac{1}{2}bh$. Computes half the product of base and height, as a triangle is half of a parallelogram with the same base and height.

Flashcard 12: State the formula for the circumference of a circle with radius $r$.

Answer: $C=2\pi r$. Multiplies the diameter by $\pi$ to find the total length around the circle.

Flashcard 13: State the formula for the volume of a cylinder with radius $r$ and height $h$.

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

Flashcard 14: Find the perimeter of a rectangle with $l=9$ and $w=4$.

Answer: $26$. Applies the perimeter formula $P=2l+2w$ by substituting the given length and width.

Flashcard 15: Find the area of a trapezoid with $b_1=8$, $b_2=14$, and $h=3$.

Answer: $33$. Averages the bases and multiplies by height per the trapezoid area formula.

Flashcard 16: State the formula for the area of 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 calculate the trapezoid's area.

Flashcard 17: State the formula for the surface area of a sphere with radius $r$.

Answer: $SA=4\pi r^2$. Multiplies four times the area of a great circle to cover the entire surface.

Flashcard 18: Find the circumference of a circle with diameter $d=12$ in terms of $\pi$.

Answer: $12\pi$. Converts diameter to radius and applies the circumference formula $C=2\pi r$.

Flashcard 19: Find the volume of a rectangular prism with $l=3$, $w=4$, and $h=5$.

Answer: $60$. Multiplies length, width, and height according to the rectangular prism volume formula.

Flashcard 20: State the formula for the volume of a 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.

Flashcard 21: State the formula for the area of a parallelogram with base $b$ and height $h$.

Answer: $A=bh$. Multiplies base by perpendicular height to find the area of the parallelogram.

Flashcard 22: State the formula for the arc length of a sector with radius $r$ and central angle $\theta$ degrees.

Answer: $s=\frac{\theta}{360}\cdot 2\pi r$. Calculates the fraction of the full circumference corresponding to the central angle in degrees.

Flashcard 23: Find the area of a circle with radius $r=5$ in terms of $\pi$.

Answer: $25\pi$. Squares the radius and multiplies by $\pi$ using the circle area formula.

Flashcard 24: State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$.

Answer: $A=\frac{1}{2}d_1d_2$. Multiplies half the diagonals, as they bisect the rhombus into four right triangles of equal area.

Flashcard 25: State the formula for the volume of a sphere with radius $r$.

Answer: $V=\frac{4}{3}\pi r^3$. Integrates the volumes of infinitesimal shells or uses the formula derived from calculus for the sphere's volume.