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A solid sphere of diameter 18 cm is melted and cast into a right circular cone whose base radius is 1/√2 times its slant height. If the radius of the sphere and the cone can are equal, then how many such cones can be made out of the sphere? 

A solid sphere of diameter 18 cm is melted and cast into a right circular cone whose base radius is 1/√2 times its slant height. If the radius of the sphere and the cone can are equal, then how many such cones can be made out of the sphere?  Correct Answer 4

Calculation:

The volume of sphere and all cones will be equal,

Let radius of sphere and cone be r cm.

V sphere = 4/3 π r3     

V cone = 1/3 π r2 h

A.T.Q

r = 1/√2 l, Multiplying by 2 and squaring both sides,

⇒ 4r2 = 2l2

⇒ 4r2 = 2(h2 + r2)

⇒ 2r2 = 2h2

⇒ r = h

∴ V cone = 1/3 π r3

1/3 π r3 = 4/3 π r3

∴ 4 cones can be made out of the sphere.

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