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 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 2: 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 3: 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 4: 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 5: 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 6: 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 7: 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 8: 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 9: 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.

Flashcard 10: 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 11: 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 12: 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 13: 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 14: 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 15: 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 16: 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 17: 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 18: 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 19: 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 20: 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 21: What is the volume of a cube with side length $s=4$?

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

Flashcard 22: 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: $\pi \times 2^2 \times 7 = 28\pi$.