Question

How does the volume of a cone change when the radius is quadrupled and the height is reduced to 1/5 of its original size?

Answer 1

The radius r is changed into 4r while the height is (1/5)h
The original volume of the cone is V = (1/3)πr²h.
The new volume of the cone becomes
V = (1/3)π(4r)²(h/5) = (4²)(1/5)(1/3)r²h = (16/5)(1/3)πr²h
Hence, the volume is changed by the factor of 16/5.