The pyramids P and Q are similar. Pyramid P has a volume of 216 cubic inches and Pyramid Q has a volume of 64 cubic inches. Find the scale factor of Pyramid P to Pyramid Q.

The correct answer is: 3 : 2

The volumes of the pyramids are given as follows:
Volume of P = 216 cubic inches
Volume of Q = 64 cubic inches
We have to find the scale factor of pyramid P to Q.
Scale factor is a ratio of length of one shape with another. It helps us compare the dimensions of the shapes.
The pyramids are similar. We will use the theorem of similar solids.
Statement: When two similar solids have length a and b then, the ratio of their areas is a²:b² and ratio of their volume is a³:b³
To find the scale factor of pyramid P to Q, we will take cube root of ratio of volume of P to volume of Q.
(scale factor)³ = Volume of P/volume of Q


So, the scale factor of pyramid P to pyramid Q is 3:2

For such questions, we should know the properties of similar objects.