SSAT Upper Level Quantitative 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 SSAT Upper Level 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: State the volume formula for a cube with side length $s$.

Answer: $V=s^3$. The volume equals the side length cubed, as all dimensions are equal.

Flashcard 2: Identify the correct volume if a cube's side doubles from $s$ to $2s$.

Answer: $V\text{ becomes }8s^3$. Doubling the side length scales the volume by $2^3 = 8$.

Flashcard 3: What is the volume of a cone with radius $r=6$ and height $h=9$?

Answer: $V=108\pi$. Take one-third of the base area times height for the cone's volume.

Flashcard 4: State the volume formula for a rectangular prism with length $l$, width $w$, and height $h$.

Answer: $V=lwh$. The volume is the product of the three perpendicular dimensions of the prism.

Flashcard 5: What is the volume of a pyramid with base area $B=48$ and height $h=9$?

Answer: $V=144$. The volume is one-third the base area multiplied by the height.

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

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

Flashcard 7: State the volume formula for a right circular cone with radius $r$ and height $h$.

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

Flashcard 8: State the volume formula for a right prism with parallelogram base area $B$ and height $h$.

Answer: $V=Bh$. The volume is the parallelogram base area times the perpendicular height.

Flashcard 9: What is the volume of a prism with base area $B=15$ and height $h=8$?

Answer: $V=120$. Multiply the base area by the height to get the prism volume.

Flashcard 10: What is the volume of a composite solid: a $3\times 3\times 8$ prism plus a $3\times 3\times 2$ prism?

Answer: $V=90$. Add the volumes of the two prisms to find the total composite volume.

Flashcard 11: Identify the correct volume scale factor if all linear dimensions triple.

Answer: $\text{Volume factor }=27$. Tripling linear dimensions scales volume by $3^3 = 27$.

Flashcard 12: What is the volume of a cylinder with diameter $10$ and height $4$?

Answer: $V=100\pi$. Use radius as half the diameter in the cylinder volume formula.

Flashcard 13: State the volume formula for a prism (any base) with base area $B$ and height $h$.

Answer: $V=Bh$. The volume is the base area extruded along the height of the prism.

Flashcard 14: State the volume formula for a right circular cylinder with radius $r$ and height $h$.

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

Flashcard 15: State the volume formula for a triangular prism with triangle base area $A$ and prism height $h$.

Answer: $V=Ah$. The volume is the triangular base area multiplied by the prism's height.

Flashcard 16: State the volume formula for a pyramid with base area $B$ and height $h$.

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

Flashcard 17: What is the volume of a sphere with diameter $10$?

Answer: $V=\frac{500}{3}\pi$. Use radius as half the diameter in the sphere volume formula.

Flashcard 18: What is the volume of a rectangular prism with $l=5$, $w=3$, and $h=4$?

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

Flashcard 19: What is the volume of a triangular prism with base area $A=12$ and height $h=7$?

Answer: $V=84$. The volume equals the triangular base area times the prism height.

Flashcard 20: What is the volume of a sphere with radius $r=3$?

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

Flashcard 21: What is the volume of a cylinder with radius $r=3$ and height $h=10$?

Answer: $V=90\pi$. Compute the base area as $\pi r^2$ and multiply by height.