Exercise 12 Page 646

We are given two prisms that are similar. The volume of the first prism is $4$ cubic meters and the volume of the second prism is $864$ cubic meters. We want to find how many times the second prism is larger than the first prism. To do so, let's start by recalling the relationship between the volumes of similar solids.

Volume of Similar Solids

If Solid $X$ is similar to Solid $Y$ by a scale factor, then the volume of $X$ is equal to the volume of $Y$ times the cube of the scale factor.

In this case, the $\text{volume}$ $\text{of}$ $\text{the}$ $\text{second}$ $\text{prism}$ is equal to the $\text{volume}$ $\text{of}$ $\text{the}$ $\text{first}$ $\text{prism}$ times the $\text{scale}$ $\text{factor}$ raised to the $\text{third}$ ${{\color{#A800DD}{\text{power}}}.$ We got an equation that will help us to find the $\text{scale}$ $\text{factor}.$ Note that the $\text{scale}$ $\text{factor}$ tells us how many times the second prism is larger than the first prism. Let's solve the equation for $x!$ Therefore, the $\text{scale}$ $\text{factor}$ is equal to $6.$ This means that the second prism is $6$ times larger than the first prism and A is the correct option.