Chapter E, Problem 12.11EX

To determine

To find: The lateral area of the larger pyramids.

Answer to Problem 12.11EX

The lateral area of the larger pyramids is $50$ .

Explanation of Solution

Given information:Two similar pyramids have volumes $27$ and $125$ .If the smaller has lateral area $18$ .

Calculation:

Let volume of first pyramids has $V_1=27$ .

And volume of second pyramids has $V_2=125$

  $\begin{array}{l}\frac{V_1}{V_2}=\frac{27}{125}\\ \frac{V_1}{V_2}=\frac{r_1{}^3}{r_2{}^3}\\ \frac{r_1{}^3}{r_2{}^3}=\frac{27}{125}\\ \frac{r_1}{r_2}=\frac{3}{5}\end{array}$

the smaller has lateral area $A_1=18$ .

Let the larger has lateral area $A_2$ .

Then

  $\begin{array}{l}\frac{A_1}{A_2}=\frac{r_1{}^2}{r_2{}^2}\\ \text{Given }\frac{r_1}{r_2}=\frac{3}{5},A_1=18\\ \frac{18}{A_2}=\frac{3^2}{5^2}\\ A_2=50\end{array}$