A solid right circular cone of diameter 14cm and height 8cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, find the internal diameter of the sphere.

The internal diameter of the sphere is 6 cm.

Step-by-step explanation:

Given that, a solid right circular cone of diameter 14 cm and height 8 cm.

The radius of the cone is

                                        = 7 cm.

The volume of the cone is

Let the internal radius of the sphere be r.

The external diameter of the sphere is = 10 cm

The external radius of the sphere is(R) = 5 cm

The volume of the sphere is

The sphere is formed by the solid right circular cone.

∴The volume of the sphere = The volume of the cone

According to the problem,

⇒r= 3

The internal radius of the sphere is = 3 cm.

The internal diameter of the given sphere is = (2×3) cm =6 cm.

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