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Rectangular Prisms: Volume & Surface Area

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Rectangular Prisms: Volume & Surface Area

Use the formulas to find each measurement. Show your calculations and include the correct units.

Volume

Volume of a rectangular prism: V = length × width × height

1.A rectangular prism is 9 feet long, 4 feet wide, and 5 feet tall. What is its volume?
2.A shipping carton has dimensions 11 inches by 7 inches by 3 inches. Find its volume.
3.A rectangular prism measures 6 yards long, 3 yards wide, and 4 yards high. Choose its volume.
  • 72 cubic yards
  • 36 cubic yards
  • 13 cubic yards
  • 144 cubic yards
4.A fish tank is 30 inches long, 10 inches wide, and 16 inches tall. How many cubic inches of water can it hold when filled to the top?

Surface Area

Surface area of a closed rectangular prism: SA = 2(length × width + length × height + width × height)

5.A closed rectangular prism is 7 feet long, 3 feet wide, and 5 feet high. Find its total surface area.
6.A closed box is 4 inches long, 9 inches wide, and 2 inches high. What is its total surface area?
  • 72 square inches
  • 112 square inches
  • 88 square inches
  • 144 square inches
  • 124 square inches
7.Eli is covering every face of a gift box that is 12 inches long, 5 inches wide, and 4 inches tall. How many square inches of paper are needed, ignoring overlaps?

Apply and Explain

For an open-top rectangular pool, count the bottom and four side walls, but not the top.

8.A rectangular pool is 20 feet long, 12 feet wide, and 5 feet deep. Find its capacity in cubic feet and the area of its bottom and four inside walls. Do not count the open top.
9.A prism has dimensions 2 units, 5 units, and 7 units. If each dimension is doubled, what is the new volume, and how does it compare with the original volume? Explain.
10.Design a rectangular prism with whole-number side lengths and a volume of exactly 84 cubic units. Draw and label it, then show multiplication to verify its volume.

3 printable pages

  • Rectangular prism volume practice with four problems.

    Page 1

  • Rectangular prism surface area calculations and gift-box context.

    Page 2

  • Pool volume and open-top surface area, scale factor reasoning, and a prism design challenge.

    Page 3

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