Question

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

Answer 1

Vcone=1/3(hpir^2)
h is 2 times diameter
diameter is 2 times radius
h is 4 times radius
h=4r
sub 4r for h

V=1/3(4rpir^2)
V=1/3(4pir^3)

Answer 2

Answer:
`(4)/(3)\pi r^3`

Explanation:

We know that the volume of a cone is given by :-

`\text{Volume}=(1)/(3)\pi r^2 h`, where r is radius and h is height of the cone.

Given: Height of cone = 2(2r)=4r , where 2r is the diameter of the cone with radiis r.

Then , the volume of the cone will be:-

`\text{Volume}=(1)/(3)\pi r^2 (4r)=(4)/(3)\pi r^3`

Hence, the volume of the cone in terms of its base radius r =
`(4)/(3)\pi r^3`