Question

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

विकल्प

•  3 V

•  4 V

• 6 V

• 8 V

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone =  `1/3 pi r^2h`= V

Since it is given that the radius and height are doubled we have the radius as ‘2r’ and the vertical height as ‘2h’

So now,

Volume of modified cone =`1/3 pi(2r)^2 (2h)` 

=`8/3pi r^2 h`

= 8V