Question

The volume of the cone shown is 5 cubic inches. What is the height of a cone with the same base diameter but a volume of 10 cubic inches?

Answer 1

The height of the second cone is 2 h₁.

Explanation:

The volume of a cone is:

`V=\pi\ r^(2)(h)/(3)`

The volume of the first cone is, V₁ = 5 in³.

The volume of the second cone is, V₂ = 10 in³.

The two cones have the same base diameters.

This implies that the two radii are same, i.e. r₁ = r₂.

Compute the height of the second cone as follows:

`r_(1)=r_(2)`

`(3\cdot V_(1))/(\pi\ h_(1))=(3\cdot V_(2))/(\pi\ h_(2))`

`(V_(1))/(h_(1))=(V_(2))/( h_(2))`

`(5)/(h_(1))=(10)/(h_(2))`

`h_(2)=2\ h_(1)`

Thus, the height of the second cone is 2 h₁.