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 =$\frac{1}{3} \pi r^{2} h$

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 = $\frac{1}{3} \pi (2r)^2 (\frac{2}{3} h)$

= $\frac{1}{3} \pi 4r^2 (\frac{2}{3} h) = \frac{8}{6} \pi r^{2} h =\frac{8}{2} (\frac{1}{3} \pi r^{2} h )$$=4*(\frac{1}{3} \pi r^{2} h )$

It means the volume becomes 4 times