Geometry · Volume and surface area

How to Find the Volume of a Rectangular Prism

Problem

4×3×54 \times 3 \times 5

Answer

V=60V = 60

A rectangular prism is a box. Its volume is the space it fills: length times width times height.

Step-by-step solution

  1. Write the volume formula.

    V=l×w×hV = l \times w \times h

    Why: Volume is the space inside a box with three dimensions.

  2. Substitute the three lengths.

    V=4×3×5V = 4 \times 3 \times 5

    Why: The order of the three numbers does not change the product.

  3. Multiply.

    V=60V = 60

    Why: 4 times 3 is 12, and 12 times 5 is 60.

  4. Add the cubic unit.

    60 cubic units60\ \text{cubic units}

    Why: Volume measures a three-dimensional space.

Common mistakes

  • Adding the lengths instead of multiplying.
  • Multiplying only two lengths. A volume uses all three.
  • Leaving the answer as a squared unit. Volume uses cubic units.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. 2×3×42 \times 3 \times 4

    Show answer

    V=24V = 24

  2. 5×5×25 \times 5 \times 2

    Show answer

    V=50V = 50

  3. 6×2×36 \times 2 \times 3

    Show answer

    V=36V = 36

  4. 10×1×710 \times 1 \times 7

    Show answer

    V=70V = 70

  5. 3×3×33 \times 3 \times 3

    Show answer

    V=27V = 27