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5. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

5. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
Number of cones will be = Volume of cylinder / Volume of ice cream cone For the cylinder part, Radius = 12/2 = 6 cm Height = 15 cm ∴ Volume of cylinder = π×r2×h = 540π For the ice cone part, Radius of conical part = 6/2 = 3 cm Height = 12 cm Radius of hemispherical part = 6/2 = 3 cm Now, Volume of ice cream cone = Volume of conical part + Volume of hemispherical part = (⅓)×π×r2×h+(⅔)×π×r3 = 36π +18π = 54π ∴ Number of cones = (540π/54π) = 10

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