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Question
A cube A has side thrice as long as that of cube B. What is the ratio of the volume of cube A to that of cube B?
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Solution
Suppose that the length of the side of cube B is l cm .
\[\text { Then, the length of the side of cube A is 3 }\times l cm . \]
\[\text { Now, ratio } = \frac{\text { volume of cube A}}{\text { volume of cube B }}=\frac{(3 \times l )^3 {cm}^3}{(l )^3 {cm}^3}=\frac{3^3 \times l^3}{l^3}=\frac{27}{1}\]
\[ \therefore \text { The ratio of the volume of cube A to the volume of cube B is 27: 1 }.\]
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