Question

The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm, respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.

Answer 1

Internal radius of hemisphere = 3 cm and external radius of hemisphere = 5 cm

Diameter of cone = 14 cm

Radius of cone = 7 cm

Now,

Volume of the hollow hemisphere = Volume of the cone

Volume of cone = 1/3 πr²h

Volume of the hollow hemisphere = 2/3 π(R³ – r³)

2/3 π(R³ – r³) = 1/3 π r² h

2/3 x 22/7 (5³ – 3³) = 1/3 x 22/7 x 72 x h

2 x 98 = 49h

or h = 4 cm

Height of the cone formed is 4 cm.