Question

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two similar solids have a scale factor of 3:4.
what is the ratio of their volumes expressed in lowest terms?
enter your answer by filling in the boxes.

Explanation:

Step1: Recall the volume ratio formula

For similar solids, if the scale factor is \(a:b\), the ratio of their volumes is \(a^{3}:b^{3}\). Here \(a = 3\) and \(b=4\).

Step2: Calculate \(a^{3}\) and \(b^{3}\)

\(a^{3}=3^{3}=3\times3\times3 = 27\), \(b^{3}=4^{3}=4\times4\times4=64\)

Answer:

\(27:64\)