Two similar pyramids have volumes of 64cm³ and 343cm³. Find is the ratio of their surface area.

The correct answer is: 16 : 49

Let the pyramids be P and Q.
The volumes of the pyramids are given as follows:
Volume of P = 64 cubic inches
Volume of Q = 343 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


The scale factor is
Ratio of surface areas =

So, the ratio of surface area of pyramid P to pyramid Q is 16:49

We should know about similar solid theorem. We should also know different cube roots and square roots.