3-D Volume - SSAT Upper Level Quantitative

1. State the volume formula for a cube with side length $s$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Study these flashcards