Question
A right circular cylinder having diameter 21 cm & height
38 cm is 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. The number of such cones to be filled with ice cream isSolution
ATQ, Volume of a right circular cylinder = 4/3ĻrĀ²h Volume of hemisphere = 2/3ĻrĀ² Volume of cone = Volume of cylinder + Volume of hemisphere = 1/3ĻrĀ²h + 2/3ĻrĀ² Given, Volume of right circular cylinder = n [Volume of cone + Volume of hemisphere] Therefore, 4/3ĻrĀ²h = n [1/3ĻrĀ²h + 2/3ĻrĀ² ] Implies, Ļ x 21Ā² x 38 = n Ļ / 3 x 7Ā² / 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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