Question

. A solid metallic cylinder of diameter 12 cm and height 15 cm is melted and recast into toys in the shape of a right circular cone mounted on a hemisphere as shown in the figure. If radii of the cone and hemisphere are each equal to 3 cm and the height of the toy is 7 cm, calculate the number of such toys that can be formed.​

Answer 1

Answer: 18

Explanation:

Diameter of cylinder = 12 cm

Radius = 6 cm

Height = 15 cm

Volume of a cylinder = πr^2h

= π x 36 x 15 cm^3

Volume of toy = volume of cone + volume of hemisphere

1/3πr^2h + 2/3πr^3

1/3πr^2 (h + 2r)

1/3π x 3 x 3 (4 + 2 x 3)

= 30π cm^3

Therefore, no of toys =

Volume of cylinder / volume of toy

36 x 15 x π / 30 x π

= 18