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Question

A cylindrical container is filled with ice-cream, whose diameter is 12cm and height is 15cm. The whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.

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Solution

Volume of cylindrical container=πR2H=π×62×15=540π
Let radius of base of conical portion be 'r', then diameter=2r
and height=2×2r=4r
10×volume of each cone=volume of container
10[13πr2h+23πr3]=540π10×13π[r2×4r+2r3]=540π
6r3=162r3=27r=327=3cm
Diameter =2r=2×3=6cm

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