ISEE Lower Level Quantitative Reasoning Flashcards: Area And Volume Relationships

What this deck covers

This deck focuses on Area And Volume Relationships, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower 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: What is the volume of a rectangular prism with $l=5$, $w=3$, and $h=2$?

Answer: $30$. Product of dimensions: $5 \times 3 \times 2 = 30$.

Flashcard 2: What is the area of a triangle with $b=12$ and $h=5$?

Answer: $30$. Half the product of base and height gives the area: $\frac{1}{2} \times 12 \times 5 = 30$.

Flashcard 3: State the formula for the circumference of a circle with radius $r$.

Answer: $C=2\pi r$. The circumference of a circle is twice pi times its radius.

Flashcard 4: A cylinder has volume $45\pi$ and radius $r=3$. What is its height $h$?

Answer: $5$. Divide volume by $\pi r^2$ to find height: $45\pi \div (\pi \times 9) = 5$.

Flashcard 5: What is the volume of a cube with side length $s=4$?

Answer: $64$. Cube the side length: $4^3 = 64$.

Flashcard 6: State the formula for the volume of a cylinder with radius $r$ and height $h$.

Answer: $V=\pi r^2h$. The volume of a cylinder is pi times the square of its radius times its height.

Flashcard 7: A cube's side length is doubled. By what factor does its volume change?

Answer: Volume is multiplied by $8$. Doubling side length scales volume by $2^3 = 8$.

Flashcard 8: A rectangle has area $48$ and width $6$. What is its length?

Answer: $8$. Divide area by width to solve for length: $48 \div 6 = 8$.

Flashcard 9: State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.

Answer: $A=\frac{1}{2}(b_1+b_2)h$. The area of a trapezoid is half the sum of its parallel bases multiplied by the height.

Flashcard 10: What is the volume of a cylinder with $r=2$ and $h=7$ in terms of $\pi$?

Answer: $28\pi$. Pi times radius squared times height: $\pi \times 2^2 \times 7 = 28\pi$.

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

Answer: $A=bh$. The area of a parallelogram is the product of its base and corresponding height.

Flashcard 12: What is the area of a circle with radius $r=3$ in terms of $\pi$?

Answer: $9\pi$. Pi times radius squared: $\pi \times 3^2 = 9\pi$.

Flashcard 13: State the formula for the area of a triangle with base $b$ and height $h$.

Answer: $A=\frac{1}{2}bh$. The area of a triangle is half the product of its base and height.

Flashcard 14: State the formula for the area of a rectangle with length $l$ and width $w$.

Answer: $A=lw$. The area of a rectangle is calculated as the product of its length and width.

Flashcard 15: What is the area of a trapezoid with $b_1=6$, $b_2=10$, and $h=4$?

Answer: $32$. Half the sum of bases times height: $\frac{1}{2} (6 + 10) \times 4 = 32$.

Flashcard 16: A rectangle's length and width are each tripled. By what factor does its area change?

Answer: Area is multiplied by $9$. Tripling dimensions scales area by $3^2 = 9$.

Flashcard 17: Identify the scale factor for area when all lengths are multiplied by $k$.

Answer: Area is multiplied by $k^2$. When linear dimensions are scaled by $k$, areas scale by the square of $k$.

Flashcard 18: Identify the scale factor for volume when all lengths are multiplied by $k$.

Answer: Volume is multiplied by $k^3$. When linear dimensions are scaled by $k$, volumes scale by the cube of $k$.

Flashcard 19: What is the area of a rectangle with $l=9$ and $w=4$?

Answer: $36$. Multiply length by width to find the area: $9 \times 4 = 36$.

Flashcard 20: State the formula for the volume of a rectangular prism with dimensions $l,w,h$.

Answer: $V=lwh$. The volume of a rectangular prism is the product of its length, width, and height.

Flashcard 21: State the formula for the area of a circle with radius $r$.

Answer: $A=\pi r^2$. The area of a circle is pi times the square of its radius.

Flashcard 22: State the formula for the volume of a cube with side length $s$.

Answer: $V=s^3$. The volume of a cube is the cube of its side length.