In the introduction, you reviewed some area formulas that you can use to calculate the area of rectangles or triangles. You also reviewed the volume formula for rectangular prisms.

In this section, you will investigate the volume formula for a rectangular prism more fully, and use the volume formula to solve problems.

Interactive exercise. Assistance may be required. Play the interactive animation below to explore the volume formula for rectangular prisms. Use what you see in the animation to answer the questions that follow.

Pause and Reflect

The number of cubes in the bottom layer is the area of the base of the prism, B. The number of layers is the height of the prism, h. Write a formula that relates the volume of the prism, V, to the area of the base of the prism, B, and the height of the prism, h.

Interactive popup. Assistance may be required.

Check Your Answer

V = BhClose Pop Up

A rectangular prism has a base with dimensions 6 centimeters by 8 centimeters and a height of 4 centimeters. What is the volume of the prism?

Interactive popup. Assistance may be required.

Check Your Answer

V = Bh, so V = (6 cm × 8 cm)(4 cm) = (48 cm2)(4 cm) = 192 cm3Close Pop Up

Practice

  1. A storage chest is shaped like a rectangular prism with the dimensions shown in the figure below.

    What is the volume of the storage chest?

    Interactive popup. Assistance may be required.

    Need a hint?

    Use the formula, V = Bh. What are the dimensions of the base of the storage chest? Close Pop Up
    Interactive popup. Assistance may be required.

    Check Your Answer

    First, determine the area of the base, B.
    B = lw = (24 in.)(12 in.) = 288 in.2

    Next, determine the volume of the prism, V.
    V = Bh = (288 in.2)(18 in.) = 5,184 in.3

    Close Pop Up
  2. A moving box in the shape of a square prism has a volume of 4.5 cubic feet. The base is a square with a side length of 18 inches. What is the height of the moving box?

    Interactive popup. Assistance may be required.

    Need a hint?

    Use the formula, V = Bh. Also, notice that the volume is in cubic feet, but the side length is in inches. You will need to convert the inches to feet or cubic feet to cubic inches before performing any calculations.

    It may also help to draw a picture.

    Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    First, convert the side length from 18 inches to feet.
    s = 18 in. × 1 ft. over 12 in. 1 ft. 12 in. = 1.5 ft

    Next, determine the area of the base, B.
    B = s × s = (1.5 ft)(1.5 ft) = 2.25 ft2

    Next, use the volume formula to relate the volume of the prism, V, to the area of the base, B.
    V = Bh
    4.5 ft3 = (2.25 ft2)(h)

    Solve the equation for h.
    4.5 ft3 = (2.25 ft2 )(h)

    4.5 ft cubed over 2.25 ft squared 4.5 ft3 2.25 ft2 = 2.25 ft. squared times h over 2.25 ft squared 2.25 ft2(h) 2.25 ft2

    2 ft = h

    The height of the box is 2 feet.

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  3. A pizza box is shaped like a rectangular prism. The base of the box has a width of 16 inches, a length of 16 inches, and the height of the box is 21 over 2 1 2 inches. To store the pizza boxes, they are stacked so that there are 12 pizza boxes in one stack, as shown in the diagram below.

    What is the combined volume of the stack of 12 pizza boxes?

    Interactive popup. Assistance may be required.

    Need a hint?

    Use the volume formula, V = Bh, to calculate the volume of one pizza box. Then, use this volume to calculate the combined volume of 12 pizza boxes. Close Pop Up
    Interactive popup. Assistance may be required.

    Check Your Answer

    First, determine the area of the base, B.
    B = lw = (16 in.)(16 in.) = 256 in.2

    Next, determine the volume of the prism (one pizza box), V.
    V = Bh = (256 in.2)( 21 over 2 1 2 in.) = 640 in.3

    Finally, determine the combined volume of the stack of 12 pizza boxes.
    V = 12 × 640 in.3 = 7,680 in.3

    The volume of the combined stack of pizza boxes is 7,680 in.3.

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