Question

Four circular cylindrical vessels, each having a diameter 21 cm and height 38 cm are full of ice-cream. This ice-cream is to be filled in cones each of height 12 cm and diameter 7 cm, having a hemispherical shape on the top. Find the total number of cones that can be filled with the ice-cream. 50 POINTS!!!​

Answer 1

Answer:

Volume of a right circular cylinder = 4/3πr²h

Volume of hemisphere = 2/3πr²

Volume of cone = Volume of cylinder + Volume of hemisphere = 1/3πr²h + 2/3πr²

Given, Volume of right circular cylinder = n [Volume of cone + Volume of hemisphere]

Therefore, 4/3πr²h = n [1/3πr²h + 2/3πr² ]

Implies, π x 21² x 38 = n π / 3 x 7² / 4 [12 + 2 x 7 / 2]

Implies, 21 x 21 x 38 = (n x 7 x 7) / 12 x 19

Implies, n = (21 x 21 x 38 x 12) / (7 x 7 x 19) = 216