Question

A student said that the volume of a cone with a 4-inch diameter is two times the volume of a cone with the same height and a 2-inch radius. What is the error?

Answer 1

Explanation:

Let V be the volume of the cone.

The student says that, the volume of a cone with a 4-inch diameter is two times the volume of a cone with the same height and a 2-inch radius.

If diameter is 4 inch, radius = 2 inch

Volume of the cone,

`V=(\pi )/(3)* 2^2* h\\\\V=(4\pi h)/(3)` .......(1)

If radius, r = 2 inch

New volume,

`V=(\pi )/(3)* 2^2* h\\\\V=(4\pi h)/(3)` ....(2)

We can see that the volume in both case is same. Hence, the student is correct.