Chapter 12, Problem 13CT

To determine

To find:The ratio of lateral areas.

Answer to Problem 13CT

The ratio of lateral areas is $100:16$ .

Explanation of Solution

Given information:

Given that the volumes of two similar rectangular solids are $1000{\text{cm}}^{\text{3}}$ and $64\text{}{\text{cm}}^{\text{3}}$ .

Calculation:

Consider the volumes of two rectangular solids.

Ratio of lateral area is equal to the $\frac{2^{\text{th}}}{3}$ root of the volume.

Calculate the ratio of lateral areas.

  $\begin{array}{l}\frac{L.A_1}{L.A_2}={\left(\frac{1000}{64}\right)}^{\frac{2}{3}}\\ \frac{L.A_1}{L.A_2}={\left(\frac{10}{16}\right)}^2\\ \frac{L.A_1}{L.A_2}=\frac{100}{16}\end{array}$

Therefore, the ratio of lateral areas is $100:16$ .