Question

A solid right circular cone or radius 4 cm and height 7 cm is melted to form a sphere. Find the radius of sphere.​

Answer 1

If a solid right circular cone of radius 4 cm and height 7 cm is melted to form a sphere.

A.T.Q

The Volume of cone = Volume of sphere

1/3πr²h = 4/3πr³

⇒ Volume of cone = 1/3×22/7×4×4×7 

= 352/3

= 117.33333 cu cm

Volume of sphere = 4/3πr³

⇒ 117.33333 = 4/3×22/7×r³

⇒ 117.33333×21 = 88r³

⇒ 2463.99993 = 88r³

⇒ r³ = 2463.99993/88

⇒ r³ = 27.9999

⇒ r = ∛27.9999

⇒ r = 3.0365 cm

Thus, radius of the sphere is 3.0365 cm.

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