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.
A
Practice makes perfect
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 volume of the second prism is equal to the
volume of the first prism times the scale factor raised to the third power.
864 = 4 * x^3
We got an equation that will help us to find the scale factor. Note that the scale factor tells us how many times the second prism is larger than the first prism. Let's solve the equation for x!
