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The volume of a cube is $42 \frac{1}{2}$ cubic centimeters. The volume of a rectangular prism is $42.7$ cubic centimeters. $\newline$ Which shape has a greater volume? $\newline$ Choices: $\newline$ (A) cube $\newline$ (B) rectangular prism

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The volume of a cube is

42 \frac{1}{2}

cubic centimeters. The volume of a rectangular prism is

42.7

cubic centimeters.

\newline

Which shape has a greater volume?

\newline

Choices:

\newline

(A) cube

\newline

(B) rectangular prism

Convert to decimal: Convert the volume of the cube from a mixed fraction to a decimal for easier comparison. $\newline$ Volume of cube = $42 \frac{1}{2}$ cubic centimeters = $42.5$ cubic centimeters.
Compare volumes: Compare the volumes of the cube and the rectangular prism. $\newline$ Volume of cube = $42.5\,\text{cm}^3$ $\newline$ Volume of rectangular prism = $42.7\,\text{cm}^3$ $\newline$ Since $42.7$ is greater than $42.5$ , the rectangular prism has a greater volume.

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