Question

How does the volume of an oblique cone change if the height is reduced to 2/3 of its original size and the radius is doubled

Answer 1

The volume of oblique cone =
`(1)/(3) \pi r^(2) h`

Now radius is doubled is now it is 2r

And height is reduced to 2/3 of its original size that is 2/3 h

So plugging the values we get volume

New Volume =
`(1)/(3) \pi (2r)^2 ((2)/(3) h)`

=
`(1)/(3) \pi 4r^2 ((2)/(3) h) = (8)/(6) \pi r^(2) h =(8)/(2) ((1)/(3) \pi r^(2) h )`
`=4*((1)/(3) \pi r^(2) h )`

It means the volume becomes 4 times