Question

Two triangular pyramids are similar. The volume of the larger pyramid is 729 cm3 , and the volume of the smaller pyramid is 64 cm3. If the perimeter of the base of the smaller pyramid is 8 cm, what is the perimeter of the base of the larger pyramid?

Answer 1

A. 18 cm is the answer 

Answer 2

The perimeter of the base of the larger pyramid is 18 cm.

Explanation:

We have been given, two triangular pyramids are similar.

Volume of larger pyramid = 729 cubic cm

Volume of smaller pyramid = 64 cubic cm

So, the ratio of volume of larger pyramid to volume of smaller pyramid is given by:

`(729)/(64)` =
`(9^(3))/(4^(3))`

Thus the ratio of side of larger pyramid to the side of smaller pyramid is given by: 9:4 or
`(9)/(4)`

Given is , the perimeter of base of smaller pyramid = 8 cm

The perimeter of base of larger pyramid will be:

`(9)/(4)=(x)/(8)`

`4x=72`

=>
`x=18` cm

Hence, the perimeter of the base of the larger pyramid is 18 cm.