If the radius of the base of a right circular cone by halved and its height be doubled , then the volume of the cone remains the same.

Explanation

If the volume of a right circular cone of radius r unit and height h unit be V cubic - unit , then `V=(1)/(3)pi r^2h`
Now , if the radius of its base be halved and its height be doubled , then the volume of the cone `=(1)/(3)pi ((r)/(2))^2.2h` cubic - unit `=(1)/(3)pi. (r^2)/(4).2h` cubic -unit `=(1)/(2).(1)/(3)pir^2h` cubic - unit `=(1)/(2)V`
i.e., the volume is halved.
Hence the given statement is false.