Mensuration-62

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Four right circular cylindrical vessels each having diameter 21 cm and height 38 cm are full of ice-cream.
The ice-cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top.
Find the total number of such cones which can be filled with ice-cream.

Solution: Volume of a right circular cylinder = 4/3 Π r2 h

Volume of hemisphere = 2/3 Π r2

Volume of cone = Volume of cylinder + Volume of hemisphere = 1/3 Π r2 h + 2/3 Π r2

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

Therefore, 4/3 Π r2 h = n [1/3 Π r2 h + 2/3 Π r2 ]

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.

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