ISEE Middle Level Mathematics Achievement Flashcards: 3 D Volume

What this deck covers

This deck focuses on 3 D Volume, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Mathematics Achievement.

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 volume of any pyramid in terms of base area $B$ and height $h$.

Answer: $V = \frac{1}{3}Bh$. The volume is one-third of the base area multiplied by the height to the apex.

Flashcard 2: State the formula for the volume of a right circular cone with radius $r$ and height $h$.

Answer: $V = \frac{1}{3}\pi r^2 h$. The volume is one-third of the base area $\pi r^2$ multiplied by the height.

Flashcard 3: What is the volume of a cylinder with radius $r = 3$ and height $h = 5$ in terms of $\pi$?

Answer: $45\pi$. Compute the base area $\pi r^2$ and multiply by height.

Flashcard 4: A cylinder has volume $72\pi$ and radius $r = 3$. What is the height $h$?

Answer: $8$. Solve for height by dividing volume by $\pi r^2$.

Flashcard 5: A rectangular prism has volume $120$, length $10$, and width $3$. What is the height $h$?

Answer: $4$. Solve for height by dividing volume by length times width.

Flashcard 6: A cone has volume $36\pi$, radius $r = 3$, and height $h$ unknown. What is $h$?

Answer: $12$. Solve for height by rearranging the cone volume formula.

Flashcard 7: State the formula for the volume of any prism in terms of base area $B$ and height $h$.

Answer: $V = Bh$. The volume is the base area multiplied by the height, which is the perpendicular distance between bases.

Flashcard 8: State the formula for the volume of a cube with side length $s$.

Answer: $V = s^3$. The volume is the side length raised to the third power, as all dimensions are equal.

Flashcard 9: State the formula for the volume of a right rectangular pyramid with base area $B$ and height $h$.

Answer: $V = \frac{1}{3}Bh$. The volume is one-third of the product of the base area and the height perpendicular to the base.

Flashcard 10: A cone and cylinder share the same base radius $r$ and height $h$. What is $\frac{V_{\text{cone}}}{V_{\text{cyl}}}$?

Answer: $\frac{1}{3}$. The cone's volume is one-third that of the cylinder with identical base and height.

Flashcard 11: What is the volume of a cube with side length $s = 6$?

Answer: $216$. Cube the side length to compute the volume.

Flashcard 12: A pyramid has volume $30$, height $5$, and base area $B$ unknown. What is $B$?

Answer: $18$. Solve for base area by rearranging the pyramid volume formula.

Flashcard 13: State the formula for the volume of a sphere with radius $r$.

Answer: $V = \frac{4}{3}\pi r^3$. The formula derives from integrating the cross-sectional area of a sphere.

Flashcard 14: State the formula for the volume of a rectangular prism with length $l$, width $w$, and height $h$.

Answer: $V = lwh$. The volume is calculated as the product of the three dimensions: length, width, and height.

Flashcard 15: What is the volume of a rectangular prism with $l = 5$, $w = 3$, and $h = 4$?

Answer: $60$. Multiply the length, width, and height to find the volume.

Flashcard 16: What is the volume of a sphere with radius $r = 3$ in terms of $\pi$?

Answer: $36\pi$. Apply the sphere volume formula with the given radius.

Flashcard 17: A cylinder has diameter $10$ and height $4$. What is its volume in terms of $\pi$?

Answer: $100\pi$. Use radius half of diameter in $\pi r^2 h$.

Flashcard 18: What is the volume of a prism with base area $B = 12$ and height $h = 7$?

Answer: $84$. Multiply the base area by the height to obtain the volume.

Flashcard 19: A sphere has diameter $12$. What is its volume in terms of $\pi$?

Answer: $288\pi$. Use radius half of diameter in $\frac{4}{3}\pi r^3$.

Flashcard 20: What is the volume of a cone with radius $r = 6$ and height $h = 3$ in terms of $\pi$?

Answer: $36\pi$. Calculate one-third of $\pi r^2$ times height.

Flashcard 21: What is the volume of a pyramid with base area $B = 27$ and height $h = 6$?

Answer: $54$. Take one-third of the product of base area and height.

Flashcard 22: What is the volume of a cylinder with radius $r = 2$ and height $h = 9$ in terms of $\pi$?

Answer: $36\pi$. Compute $\pi r^2 h$ with the given values.

Flashcard 23: What is the volume of a triangular prism with base area $B = 15$ and prism height $h = 8$?

Answer: $120$. Multiply the triangular base area by the prism height.

Flashcard 24: A cone has diameter $8$ and height $9$. What is its volume in terms of $\pi$?

Answer: $48\pi$. Use radius half of diameter in $\frac{1}{3}\pi r^2 h$.

Flashcard 25: State the formula for the volume of a right circular cylinder with radius $r$ and height $h$.

Answer: $V = \pi r^2 h$. The volume is the base area $\pi r^2$ multiplied by the height.