How do you keep the volume of a cylinder the same if the radius quadruples?

V = pi r^2*H

&

V = pi (4r)^2*h

Equate

pi r^(2)H= pi (4r)^2 h

pi cancel down

r^(2)H = (4r)^2h

r^(2)*H = 16r^(2)*h

'r^(2) cancels down

H= 16h

h = H/16

This means is you increase the radius by '4 times' , then you reduce the height(H) by '16 times' in order to maintain the same volume.