Question

If the height and radius of a cone of volume V are doubled, then the volume of a cone is?

Answer 1

Let radius of cone = r cm

and, height of cone = h cm



Now, radius and height of cone of volume V are double.

So, Radius of new cone = 2r cm

And, height of new cone = 2h cm

Therefore,

Hence, Volume of new cone is 8 times the original cone.

Answer 2

Given:

The height and radius of a cone is doubled

To find:

The volume of the cone

Solution:

The volume of a cone is 8/3π$R^{2}$H.

We can find the volume of the cone by following the process given below-

Let us make the following assumptions-

The height of the given cone is H and the radius of the cone is R.

We know that the volume of a cone, V=1/3π$R^{2}$H

Now, it is given to us that the height and radius have been doubled.

Since the old dimensions have been changed, the new volume will increase multifold.

The new height of the cone=2H

The new radius of the cone=2R

Putting the new values, we get

The new volume of the cone=1/3π(2$R^{2}$)(2H)

=1/3π×$4R^{2}$×2H

=8/3π$R^{2}$H

=8V

The new volume obtained is 8 times the old volume of the cone.

Therefore, the volume of a cone is 8/3π$R^{2}$H.