Question

A cylinder and a cone have the same volume. The cylinder has a radius of 8 inches and a height of 6 inches. The cone has a radius of 12 inches. What is the height of the cone?

Answer 1

Answer:
`8\ in.`

Explanation:

Given

Radius and height of cylinder is 8 and 6 inches

Similarly the radius of cone is 12 inches

If they have same volume

Equate the volume of cylinder and cone

`\Rightarrow \pi r^2h=(1)/(3)\pi r'^2h'\\\\\Rightarrow \pi \cdot 8^2* 6=(1)/(3)\pi \cdot 12^2* h\\\\\Rightarrow h=(64* 18)/(144)\\\\\Rightarrow h=8\ in.`

Therefore , the height of cone is 8 in.