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 36 inches and a height of 24 inches. How many times bigger is the volume of pyramid B than pyramid A?

Question

xapproachesinfinity · Answer

the side length and height were increased by the factor of 3
so you would have volume also increased by a factor of 3^3

xapproachesinfinity · Answer

Volume of a pyramid $V=B^2H/3$
B=3b
H=3h
where B is the base length of the large pyramid
and H is its height 
so $V=9b^23h/3=9b^2h=(3^2)b^2h$