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Question
What will happen to the volume of a cube, if its edge is trebled?
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Solution
\[\text { Suppose that the length of the edge of the cube is x } . \]
\[\text { Then, volume of the cube = (side ) }^3 = x^3 \]
\[\text { When the length of the side is trebled, the length of the new edge becomes 3 } \times x . \]
\[\text { Now, volume of the new cube = (side ) }^3 = (3 \times x )^3 = 3^3 \times x^3 = 27 \times x^3 \]
\[\text { Thus, if the edge of a cube is trebled, its new volume will be 27 times the initial volume } .\]
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