Apply Volume Formulas to Prisms - 5th Grade Math

1. What is the base area $b$ if a prism has $V=84$ and height $h=7$ in $V=b\times h$?

   $b = 12$ square units. Divide volume by height: $84 \div 7 = 12$.

2. What is the width $w$ if $V=72$, $l=8$, and $h=3$ in $V=l\times w\times h$?

   $w = 3$ units. Rearrange to $w = V \div (l \times h) = 72 \div 24 = 3$.

3. Find the volume of a prism with base area $b=25$ square units and height $h=2$ units.

   $50$ cubic units. Apply $V = 25 \times 2 = 50$.

4. A right rectangular prism has volume $V=96$. If $l=8$ and $w=4$, what is $h$?

   $h = 3$ units. Solve $96 = 8 \times 4 \times h$ for $h$.

5. Identify the base area $b$ when $l=6$ and $w=2$ for a rectangular prism.

   $b = 12$ square units. Base area equals length times width: $6 \times 2 = 12$.

6. Identify the volume of a prism with base area $b = 15$ and height $h = 4$.

   $60$ cubic units. Apply $V = 15 \times 4 = 60$.

7. State the volume formula for a right rectangular prism using base area and height.

   $V = b \times h$. Base area times height gives volume.

8. What is the length $l$ if $V=90$, $w=5$, and $h=3$ in $V=l\times w\times h$?

   $l = 6$ units. Rearrange to $l = V \div (w \times h) = 90 \div 15 = 6$.

9. A prism has base area $b=9\ \text{m}^2$ and height $h=6\ \text{m}$. What is $V$?

   $54\ \text{m}^3$. Apply $V = 9 \times 6 = 54$ cubic meters.

10. A storage bin is $4$ ft by $3$ ft by $2$ ft. What volume of space does it hold?

    $24\ \text{ft}^3$. Apply $V = 4 \times 3 \times 2 = 24$ cubic feet.

11. A box is $5$ ft long, $4$ ft wide, and $3$ ft high. What is its volume?

    $60\ \text{ft}^3$. Apply $V = 5 \times 4 \times 3 = 60$.

12. Find and correct the error: A student wrote $V = b + h$ for a rectangular prism.

    Correct: $V = b \times h$. Volume uses multiplication, not addition.

13. Identify the volume of a prism with $l = 9$, $w = 2$, and $h = 1$.

    $18$ cubic units. Apply $V = 9 \times 2 \times 1 = 18$.

14. A storage bin has base area $b=18\ \text{in}^2$ and height $h=5$ in. What is its volume?

    $90\ \text{in}^3$. Apply $V = 18 \times 5 = 90$.

15. What is the volume of a prism with $l=4$, $w=3$, and $h=2$?

    $24$ cubic units. Apply $V = 4 \times 3 \times 2 = 24$.

16. Find and correct the error: A student wrote $V = l + w + h$ for prism volume.

    Correct: $V = l \times w \times h$. Volume uses multiplication, not addition.

17. Identify the missing height $h$ if $V = 72$ and $b = 9$ in $V = b \times h$.

    $h = 8$. Solve $72 = 9 \times h$ by dividing both sides by 9.

18. Find the missing width if $V=90$, $l=5$, and $h=3$ (units).

    $w = 6$ units. Solve $90 = 5 \times w \times 3$ for $w$.

19. What is the volume of a prism with $l=7$, $w=2$, and $h=4$?

    $56$ cubic units. Apply $V = 7 \times 2 \times 4 = 56$.

20. Which expression correctly represents the volume when $l=9$, $w=2$, and $h=5$?

    $V = 9 \times 2 \times 5$. Volume formula uses multiplication of dimensions.

21. If the base is $l \times w$ and the height is $h$, what is $V$ written using $b$?

    $V = b \times h$ with $b = l \times w$. Substitute base area for length times width.

22. Identify the volume of a prism with $l = 7$, $w = 6$, and $h = 2$.

    $84$ cubic units. Apply $V = 7 \times 6 \times 2 = 84$.

23. Identify the base area if a prism has $l=6$ units and $w=5$ units.

    $b = 30$ square units. Base area equals $l \times w = 6 \times 5$.

24. Find the missing height if $V=72$ cubic units and base area $b=9$ square units.

    $h = 8$ units. Divide volume by base area: $72 \div 9 = 8$.

25. Find the volume of a prism with $l=4$, $w=3$, and $h=2$ (units).

    $24$ cubic units. Apply $V = 4 \times 3 \times 2 = 24$.

26. Identify the volume of a prism with $l = 10$, $w = 3$, and $h = 2$.

    $60$ cubic units. Apply $V = 10 \times 3 \times 2 = 60$.

27. Identify the missing width $w$ if $V = 84$, $l = 7$, and $h = 4$.

    $w = 3$. Solve $84 = 7 \times w \times 4$ to get $w = 3$.

28. Find the missing length if $V=48$, $w=4$, and $h=3$ (units).

    $l = 4$ units. Solve $48 = l \times 4 \times 3$ for $l$.

29. Find the volume of a prism with base area $b=20$ square units and height $h=4$ units.

    $80$ cubic units. Apply $V = 20 \times 4 = 80$.

30. Identify the volume of a box $5$ ft by $4$ ft by $3$ ft.

    $60\ \text{ft}^3$. Apply $V = 5 \times 4 \times 3 = 60$ cubic feet.

31. State the volume formula for a right rectangular prism using length, width, and height.

    $V = l \times w \times h$. Multiply all three dimensions to find volume.

32. Identify the error: A student says $V = l + w + h$ for a rectangular prism. What is correct?

    $V = l \times w \times h$. Volume requires multiplication, not addition of dimensions.

33. A prism has base area $b=12$ square units and volume $V=60$ cubic units. Find $h$.

    $h = 5$ units. Divide volume by base area: $60 \div 12 = 5$.

34. What does $b$ represent in the formula $V = b \times h$ for a rectangular prism?

    $b$ is the area of the base. In this formula, base area replaces $l \times w$.

35. A prism has $l=3$, $w=3$, and $h=3$. What is its volume?

    $27$ cubic units. A cube with side 3: $V = 3 \times 3 \times 3 = 27$.

36. Find and correct the error: A student wrote $V = l + w + h$ for a rectangular prism.

    Correct: $V = l \times w \times h$. Volume uses multiplication, not addition of dimensions.

37. What is the volume of a prism with base area $b=12$ and height $h=5$?

    $60$ cubic units. Apply $V = 12 \times 5 = 60$.

38. Identify the volume of a fish tank with base $6$ in by $4$ in and height $5$ in.

    $120\ \text{in}^3$. Apply $V = 6 \times 4 \times 5 = 120$ cubic inches.

39. Identify the missing length $l$ if $V = 60$, $w = 5$, and $h = 3$.

    $l = 4$. Solve $60 = l \times 5 \times 3$ to get $l = 4$.

40. A prism has $l=9$ units and $w=4$ units. What is the base area $b$?

    $b = 36$ square units. Base area equals $l \times w = 9 \times 4$.

41. What unit is used for volume if the edge lengths are measured in centimeters?

    cubic centimeters, $\text{cm}^3$. Volume units are always cubed length units.

42. Which expression correctly represents the volume of a prism with $l = 8$, $w = 2$, $h = 5$?

    $V = 8 \times 2 \times 5$. Shows the multiplication before calculating.

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

    $24$ cubic units. Apply $V = 4 \times 3 \times 2 = 24$.

44. Find the missing height $h$ for a prism with $l=5$, $w=4$, and $V=100$.

    $h = 5$ units. Rearrange to $h = V \div (l \times w) = 100 \div 20 = 5$.

45. What is the height $h$ if $V=48$ and base area $b=16$ in $V=b\times h$?

    $h = 3$ units. Divide volume by base area: $48 \div 16 = 3$.

46. Which expression correctly represents the volume when $l=8$, $w=3$, and $h=2$?

    $8 \times 3 \times 2$. Volume formula requires multiplication, not addition.

47. What is the volume of a box measuring $10$ in by $2$ in by $3$ in?

    $60\ \text{in}^3$. Apply $V = 10 \times 2 \times 3 = 60$ cubic inches.

48. Find the volume of a prism with $l=7$, $w=2$, and $h=3$ (units).

    $42$ cubic units. Apply $V = 7 \times 2 \times 3 = 42$.

49. Identify the base area $b$ if $V = 96$ and $h = 6$ in $V = b \times h$.

    $b = 16$ square units. Solve $96 = b \times 6$ by dividing both sides by 6.

50. What is the volume unit for a prism measured in centimeters (cm)?

    cubic centimeters ($\text{cm}^3$). Volume uses cubic units of the linear measurement.

51. Identify the volume of a prism with base area $b = 18$ and height $h = 2$.

    $36$ cubic units. Apply $V = 18 \times 2 = 36$.

52. What is the base area $b$ if a prism has $l = 6$ and $w = 5$?

    $30$ square units. Base area equals $l \times w = 6 \times 5$.

53. What unit is used for volume when edge lengths are measured in centimeters?

    cubic centimeters, $\text{cm}^3$. Volume units are always cubed length units.

54. Find the volume of a prism with $l=10$ units, $w=1$ unit, and $h=6$ units.

    $60$ cubic units. Apply $V = 10 \times 1 \times 6 = 60$.

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