Exercise 24 Page 648

We are given two similar solids.

We want to find the ratio of the surface area of the larger pyramid to the smaller pyramid. Let's start by calculating the ratio of their corresponding edge lengths. We got that the dimensions of the larger pyramid is larger by a scale factor of $\frac{5}{3}$ than the dimensions of the smaller pyramid. Next, let's recall the relationship between the surface areas of similar solids.

Surface Area of Similar Solids

If Solid $X$ is similar to Solid $Y$ by a scale factor, then the surface area of $X$ is equal to the surface area of $Y$ times the square of the scale factor.

Therefore, to get the $\text{surface}$ $\text{area}$ $\text{of}$ $\text{the}$ $\text{larger}$ $\text{pyramid},$ we need to multiply the $\text{surface}$ $\text{area}$ $\text{of}$ $\text{the}$ $\text{smaller}$ $\text{pyramid}$ by $\frac{5}{3}$ raised to the $\text{second}$ $\text{power}.$ We can rewrite this equation to get the ratio of the $\text{surface}$ $\text{area}$ $\text{of}$ $\text{the}$ $\text{larger}$ $\text{pyramid}$ to the $\text{smaller}$ $\text{pyramid}.$ We got that the ratio of the $\text{surface}$ $\text{area}$ $\text{of}$ $\text{the}$ $\text{larger}$ $\text{pyramid}$ to the $\text{smaller}$ $\text{pyramid}$ is $\frac{25}{9}.$ This means that the correct option is C.