A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8:5, determine the ratio of the radius of the base to the height of either of them.
CSAofcylinderCSAofcone=85
⇒2πrhπrl=85⇒hl=45⇒5h=4l⇒5h=4√h2+r2
Squaring both sides, we get
25h2=16(h2+r2)⇒9h2=16r2⇒h2r2=169
⇒hr=√169=43=4:3orrh=34=3:4