Answer to Question #124938 in Geometry for Jonathan

Question

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?

Answer 1

 volume of the square pyramid is:

V = s²h/3

where s=side length and h= height

for square pyramid A

h(a)= 8in and s(a)=12in

volume of square pyramid for A =

V(a)=s²(a) h(a)/3

V(a)=12² . 8/3 $\implies$ 144 . 8/3 $\implies$ 1152/3 $\implies$ 384 in³

for square pyramid B

h(b)=24in and s(b)=36in

volume of square pyramid for B =

V(b)=s²(b) h(b)/3

V(b)=36² . 24/3 $\implies$ 1296 . 24/3 $\implies$ 31104/3 $\implies$ 10368 in³

We want to know how many times the volume of pyramid B is bigger than pyramid A :

= V(b)/V(a)

=10368/384

= 27 times