Question

If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Let the radius of a right circular cone be r and height of a right circular cone be h.

Then, the volume of a right circular cone = `1/3 pir^2 h`

Now, `r = r/2, h = 2h`

New volume of a right circular cone = `1/3 pi(r/2)^2 xx (2h)`

= `1/3 pi xx r^2/4 xx 2h`

= `1/3 pi xx r^2/2 h`

= `1/2(1/3 pir^2 h)`

Hence, the new volume of a right circular cone becomes half of original volume of a right circular cone.