Question

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

Answer 1

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Answer 2

Given - Radius of sphere = 5 cm

Radius of cone = 4 cm

Find - Height of cone

Solution - The surface area of sphere = 2πr². The curved surface area of cone = πrl. Here, r is radius and l is slant height of cone.

Equating the given surface area of both objects as per question.

4*22/7*5*5 = 5*22/7*4*l

Length = 5 centimetres

Now calculating the height of cone -

l² = h² + r²

5² = h² + 4²

h² = 25 - 16

h² = 9

height = ✓9

height = 3 centimetres

Therefore, the height of the cone is 3 centimetres.