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23

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 S_{1} = 2π*rh*

For cone, we have

Slant height *l =*

*S*_{2} = π*rl* =π*r*

We have,

= =

==

(squaring both side )

= =

= 100*h*^{2} = 64*r*^{2}+64*h*^{2}

= 36*h*^{2} = 64*r*^{2}

(Square root both side )

= 6h = 8r

==