Question

The ratio if the base edges of two similar pyramids is 3:4 the volume of the larger pyramid is 320 in^3. What is the volume of the smaller pyramid???

Answer 1

135 cubic inches.

Explanation:

Given : The ratio of the base edges of two similar pyramids is 3:4

The volume of the larger pyramid is 320 cubic inches.

To Find: What is the volume of the smaller pyramid?

Solution:

The ratio of the base edges of two similar pyramids is 3:4

The volume of the larger pyramid is 320 cubic inches.

The ratio of the volume of pyramids is equal to the ratio of the cubes of the sides of pyramids .

So,
`(3^3)/(4^3) =\frac{\text{Volume of smaller pyramid}}{320}`

`(27)/(64) =\frac{\text{Volume of smaller pyramid}}{320}`

`(27)/(64) * 320 =\text{Volume of smaller pyramid}`

`135 =\text{Volume of smaller pyramid}`

Thus the volume of smaller pyramid is 135 cubic inches.

Answer 2

ratio of voljumes = 3^3 : 4^3 or 27:64 small/large = 27 / 64 vol of smaller = 27 * 320 / 64 =135