Volume & Surface Area - ACT Math

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

   $V = 216$. Using $V = s^3$ with $s = 6$.

2. Identify the formula for the lateral surface area of a cone.

   $LSA = \pi r l$. Curved surface area excluding the base circle.

3. Calculate the volume of a cylinder with diameter $10$ and height $7$.

   $V = 175 \pi$. Diameter 10 means radius 5, so $V = \pi(5^2)(7)$.

4. What is the surface area of a cube with side length $7$?

   $SA = 294$. Using $SA = 6s^2$ with $s = 7$.

5. State the formula for the lateral surface area of a cylinder.

   $LSA = 2 \pi r h$. Curved surface area excluding circular bases.

6. What is the formula for the volume of a cone?

   $V = \frac{1}{3} \pi r^2 h$. One-third of cylinder volume with same base and height.

7. Find the lateral surface area of a cylinder with radius $4$ and height $10$.

   $LSA = 80 \pi$. Using $LSA = 2\pi rh$ with given values.

8. Calculate the volume of a sphere with radius $3$.

   $V = 36 \pi$. Using $V = \frac{4}{3}\pi r^3$ with $r = 3$.

9. What is the surface area of a cylinder with $r = 3$ and $h = 4$?

   $SA = 42 \pi$. Using $SA = 2\pi r(r + h)$ with given values.

10. Find the volume of a pyramid with base area $6$ cm$^2$ and height $4$ cm.

    Volume = $8\text{cm}^3$. $\frac{1}{3} \times 6 \times 4 = 8$.

11. What is the lateral surface area of a cone with radius $r=3$ and slant height $l=5$?

    $LSA = 15 \pi$. Using $LSA = \pi rl$ with given values.

12. State the formula for the surface area of a sphere.

    $SA = 4 \pi r^2$. Four times the area of a great circle.

13. What is the volume of a cylinder with $r = 2$ and $h = 5$?

    $V = 20 \pi$. Using $V = \pi r^2 h$ with given values.

14. Calculate the volume of a cube with side length $8$.

    $V = 512$. Using $V = s^3$ with $s = 8$.

15. Find the surface area of a cube with side length $4$.

    $SA = 96$. Using $SA = 6s^2$ with $s = 4$.

16. Find the surface area of a rectangular prism with $l=3$, $w=4$, $h=5$.

    $SA = 94$. Using $SA = 2(lw + lh + wh)$ with given dimensions.

17. Identify the formula for the volume of a cylinder.

    $V = \pi r^2 h$. Base area times height for circular base shape.

18. State the formula for the surface area of a cube.

    Surface Area = $6s^2$, where $s$ is the side length. Six faces, each area $s^2$.

19. What is the formula for the surface area of a cube?

    $SA = 6s^2$. Six identical square faces, each with area $s^2$.

20. Find the volume of a cone with base radius $r=4$ and height $h=9$.

    $V = 48 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.

21. What is the formula for the volume of a cube?

    Volume = $s^3$, where $s$ is the side length. Cube volume is side cubed.

22. What is the volume of a pyramid with base area $B=9$ and height $h=4$?

    $V = 12$. Using $V = \frac{1}{3}Bh$ with given values.

23. Find the volume of a cube with side $4$ cm.

    Volume = $64 \text{cm}^3$. $4^3 = 64$.

24. What is the formula for the volume of a pyramid?

    Volume = $\frac{1}{3}\text{base area} \times \text{height}$. One-third base area times height.

25. What is the formula for the surface area of a cylinder?

    $SA = 2 \pi r (r + h)$. Two circular bases plus lateral surface area.

26. Identify the volume formula for a triangular prism.

    Volume = $\text{base area} \times \text{height}$. Base area times height.

27. What is the formula for the volume of a prism?

    Volume = $\text{base area} \times \text{height}$. Base area times height.

28. What is the formula for the volume of a rectangular prism?

    Volume = $lwh$, where $l$, $w$, and $h$ are dimensions. Length times width times height.

29. Identify the formula for the volume of a sphere.

    $V = \frac{4}{3} \pi r^3$. Four-thirds times pi times radius cubed.

30. State the formula for the volume of a pyramid.

    $V = \frac{1}{3} B h$. One-third of base area times height.

31. Calculate the surface area of a pyramid with base area $9$ cm$^2$ and side area $12$ cm$^2$.

    Surface Area = $21\text{cm}^2$. $9 + 12 = 21$.

32. Identify the formula for the total surface area of a cone.

    $SA = \pi r (r + l)$. Base area plus lateral surface area of cone.

33. Calculate the volume of a cone with $r = 3$ and $h = 7$.

    $V = 21 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.

34. Find the volume of a triangular prism with base area $5$ cm$^2$ and height $10$ cm.

    Volume = $50\text{cm}^3$. $5 \times 10 = 50$.

35. How do you calculate the surface area of a rectangular prism?

    $SA = 2lw + 2lh + 2wh$. Sum of areas of all six rectangular faces.

36. Find the volume of a prism with base area $7$ cm$^2$ and height $5$ cm.

    Volume = $35\text{cm}^3$. $7 \times 5 = 35$.

37. State the formula for the surface area of a rectangular prism.

    Surface Area = $2lw + 2lh + 2wh$. Sum of areas of all six faces.

38. Find the surface area of a sphere with radius $5$.

    $SA = 100 \pi$. Using $SA = 4\pi r^2$ with $r = 5$.

39. State the formula for the surface area of a pyramid.

    Surface Area = $\text{base area} + \text{side area}$. Base plus all triangular faces.

40. Calculate the surface area of a cube with side $3$ cm.

    Surface Area = $54 \text{cm}^2$. $6 \times 3^2 = 54$.

41. What is the surface area of a sphere with diameter $10$?

    $SA = 100 \pi$. Diameter 10 means radius 5, so $SA = 4\pi(5^2)$.

42. State the surface area formula for a prism.

    Surface Area = $2\text{base area} + \text{perimeter} \times \text{height}$. Two bases plus lateral faces.

43. Find the volume of a rectangular prism with $l=2$, $w=3$, $h=4$.

    $V = 24$. Using $V = l \times w \times h$ with given dimensions.

44. State the formula for the volume of a rectangular prism.

    $V = l \times w \times h$. Multiply length, width, and height to find 3D space.

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