Write whether True or False and justify your answer

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

Let original radius of right circular cone = R

And original height of right circular cone = H

Volume in this case is given by,

Volume = 1/3 πR²H …(i)

The radius is then halved, radius (say, r) = R/2

And height is doubled, height (say, h) = 2H

Now, volume is given by

Volume’ = 1/3 πr²h

⇒ …(ii)

By comparing equations (i) and (ii), we can clearly see that Volume ≠ Volume’

Thus, Volume will not remain unchanged.

Hence, it is false.