Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with a base side length of 48 inches and a height of 32 inches. How many times bigger is the volume of pyramid B than pyramid A?

Question

alekos · Answer

Volume of a square pyramid is 

$$a^{2}h/3$$

where a is the base length and h is the height

mrnood · Answer

the side and the height are both 4 times bigger, i.e. the larger pyramid is 'similar' to the smaller and is a linear scale of 4 times bigger.

When you scale the linear dimension by a factor of n then the volume is scaled by n^3

in this case n= 4, so work out th volume scale factor from n^3