Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is meltedinto a cone of base diameter 8 cm . Find the height of the cone.

Answer 1

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Given : Internal diameter of hollow sphere(d)= 4 cm.

Internal radius of hollow sphere (r) = 4/2= 2 cm

external diameter of hollow sphere (D) = 8 cm.

external radius of hollow sphere( R )= 8/2= 4 cm.

Volume of the Hollow sphere = 4/3π(R³ - r³)

Volume of the Hollow sphere = 4/3π(4³ - 2³)

Volume of the Hollow sphere = 4/3π(64 - 8)

Volume of the Hollow sphere = 4/3π(56) cm³

Diameter of the cone(d1) = 8 cm

radius of the cone( r1)= 8/2 = 4 cm

Let the height of the cone be h cm.

Volume of the cone = ⅓ πr1²h

= ⅓ π × 4² × h = 16πh/3

Volume of the cone = Volume of the hollow sphere

16πh/3 = 4/3π(56)

16h = 4 ×56

h = (4 × 56)/16

h = 56/4 = 14 cm

Hence, the height of the cone is 14 cm.

Answer 2

Answer:

external diameter of hollow sphere (D) = 8 cm. external radius of hollow sphere( R )= 8/2= 4 cm. Let the height of the cone be h cm. Hence, the height of the cone is 14 cm.Mar 27, 2017