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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
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. |
LHS/4=RHS/4
Cancel out common factors
Simplify quotient
Calculate quotient
3LHS=3RHS
Calculate root
3a3=a
Rearrange equation