A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, Show that the radius of each is to the height of each as 3 : 4.
For cylinder, we have
Base radius = r
Height = h
∴ Curved surface area S1 = 2πrh
For cone, we have
Slant height l = 
S2 = πrl =πr
We have,
= 
=
=
= 
(squaring both side )
= 
=
= 100h2 = 64r2+64h2
= 36h2 = 64r2
(Square root both side )
= 6h = 8r
=
=
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