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.
300.8 cubic meters
Practice makes perfect
We are given two spheres that are similar in shape. We want to find the volume of the larger sphere knowing that the volume of the smaller sphere is 126.9 cubic meters. 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.
We are given that the scale factor between the two spheres is 34. Note that the scale factor is less than 1. This means that the dimensions of the larger sphere are smaller by a scale factor of 34 than the dimensions of the larger sphere. Therefore, if we multiply the volume of the larger sphere by 34 raised to the third power, we will get the volume of the smaller sphere.
x * ( 34 )^3 = 126.9
Note that we got an equation that will help us to find the volume of the larger sphere. Let's solve the equation for x!
