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Question

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone.

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Solution

Let h cm be the height of cone and l cm be its slant height.
Radius of the sphere=5 cm
Radius of the cone = 4 cm

Now, surface area of the sphere = 5(Curved surface area of the cone)
4π×52=5×(π×4×l)l=5 cmHence, height h=l2-r2=25-16=9=3 cm Volume of the cone =13π×42×3 =22×167 =50.3 cm3

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