A sphere of diameter 15.6 cm is melted and cast into a right circular

1.	A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. Find the diameter of the base of the cone.
Answer» It is given that Diameter of the sphere = 15.6 cm Radius of the sphere = 15.6/2 = 7.8 cm Height of the cone = 31.2 cm We know that 4/3 πR³ = 1/3 πr²h So we get 4/3 × (22/7) × 7.8³ = 1/3 × (22/7) × r² × 31.2 On further calculation r² = (4/3 × (22/7) × 7.8³)/ (1/3 × (22/7) × 31.2) So we get r² = (4 × 474.552)/ 31.2 = 60.84 By taking square root on the RHS r = 7.8cm Diameter = 2 (7.8) = 15.6cm Therefore, the diameter of the base of the cone is 15.6cm.

A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. Find the diameter of the base of the cone.

Answer»

It is given that

Diameter of the sphere = 15.6 cm

Radius of the sphere = 15.6/2 = 7.8 cm

Height of the cone = 31.2 cm

We know that

4/3 πR³ = 1/3 πr²h

So we get

4/3 × (22/7) × 7.8³ = 1/3 × (22/7) × r² × 31.2

On further calculation

r² = (4/3 × (22/7) × 7.8³)/ (1/3 × (22/7) × 31.2)

So we get

r² = (4 × 474.552)/ 31.2 = 60.84

By taking square root on the RHS

r = 7.8cm

Diameter = 2 (7.8) = 15.6cm

Therefore, the diameter of the base of the cone is 15.6cm.