Question

How does the volume of an oblique cone change if the height is reduced to 2/5 of its original size and the radius is doubled?

Answer 1

Option (D) is correct.

Explanation:

Let the initial original height of the cone is h and radius is r.

The volume of original cone is given by

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

Now the new height be h' = 2/5 h and radius r' = 2r

So, the new volume be

`V'=(1)/(3)* \pi r'^(2)* h'`

`V'=(1)/(3)* \pi*  2r^(2)* (2)/(5)h`

`V=(8)/(15)* \pi * r^(2)h`

Answer 2

Given that the height is reduced by 2/5 and the radius is doubled, the new volume will be given by:
V=1/3πr^2h
r=2r
h=2/5h
thus;
V=1/3*π*(2r)^2(2/5h)
=8/15πr^2h
This implies that the new volume will be 8/15 of the original volume