Question

If the lateral areas of two similar prisms are in a ratio of 8 to 18, 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 ration of the lateral areas of the smaller prism to the larger prism is 8 to 18

The first step is t find the scale factor. Recall,

area = square of scale factor

Thus, scale factor = square root of area

Thus,

`\begin{gathered} \text{scale factor = }\sqrt[]{(8)/(18)} \\ \text{Dividing the numerator and denominator by 2, we have} \\ \text{scale factor = }\sqrt[]{(4)/(9)} \\ scale\text{ factor = 2/3} \end{gathered}`

Volume = cube of scale factor. Thus,

`\begin{gathered} \text{volume = (}(2)/(3))^3 \\ \text{Volume = }(8)/(27) \\ \end{gathered}`