Question

If a sphere has the same surface area as the total surface area of a circular cone of height 40 cm and radius 30 cm, find the radius of the sphere.

Answer 1

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Given:

The height of the cone = 40cm

And radius of cone = 30cm

So,

l = √40×40+30×30

= 50cm

According to the question,

Surface area of sphere = total surface of cone

4πr^2 = πr(l+r)

4r^2 = 30×80

r^3 = 600

r= √600

= 10√6cm