Question

If the lateral areas of two similar prisms are in a ratio of 32 to 72, what is the ratio of the volumes? Enter answers in the same format and order as the original ratio. Round any decimals to the nearest 10th.

Answer 1

The Solution:

The correct answer is 8:27 or 8 to 27.

Given that the lateral areas of two similar prisms have the ratio below:

$32\colon72$

We are required to find the ratio of their volumes in the same format and order as the above-given ratio.

Step 1:

We shall find the ratio of their side lengths.

$\begin{gathered} \sqrt[]{32}\colon\text{ }\sqrt[]{72} \\ \sqrt[]{16\times2}\colon\text{ }\sqrt[]{36\times2} \\ 4\text{ }\sqrt[]{2}\colon6\text{ }\sqrt[]{2} \\ 2\colon3 \end{gathered}$

Step 2:

We shall find the ratio of their volumes.

$\begin{gathered} 2^3\colon3^3 \\ 8\colon27 \end{gathered}$

Thus, the ratio of their volumes is 8 to 27.

Therefore, the correct answer is 8:27 or (8 to 27)