Q. 665.0( 1 Vote )

# A hollow metallic Sphere with external diameter8cm and internal diameter 4cm is melted and moulded into a cone having base diameter 8cm. The height of the cone isA. 12 cmB. 14 cmC. 15 cmD. 18 cm

Given: A hollow metallic Sphere with external diameter8cm and internal diameter 4cm

A cone having base diameter 8cm

Radius of the cone is: = 4cm

External Radius of the sphere is = 4cm

Internal Radius of the sphere is = 2cm

Volume of a Hollow Sphere is given by: π((r1)3 – (r2)3) (here r1 and r2 are External and internal radii of the hollow sphere respectively)

Let V1 be the Volume of the Hollow sphere.

V1 = π((r1)3 – (r2)3)

V1 = π((4)3 – (2)3) = π(64 – 8) = π(56)

Volume of the cone is given by × π × r2 × h

Let V2 be the volume of the cone

V2 = × π × r2 × h

V2 = × π × (4)2 × h

Here, Hollow sphere is melted and moulded into a cone.

V1 = V2 π(56) = × π × (8)2 × h × π × 16 × h = × π × (56)

h = = 14cm

Height of the cone is 14cm

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