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?

Question

asked Oct 25, 2022 43.8k views

1 Answer

AiD · Answer 1 · 2022-11-01T10:08:51+0000

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.