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Geometry: Mensuration: Miscellaneous Example
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Mensuration: Miscellaneous Example
Example: A cylindrical container of radius 8 cm and height 20 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone.
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Solution: Let the radius of the base of the conical portion be r cm.
Then, height of the conical portion = 4r cm.
Volume of cone with hemispherical top = Volume of the cone + Volume of the hemispherical top
=(1/3 r2 x 4r + 2/3r3) cm3
= (6/3 r3)cm3
= (2r3).

Volume of 10 cones with hemispherical tops = (10 x 2 r3 ) cm3 = 20r3 cm3.
Volume of the cylindrical container - ( x 82 x 20) cm3 = 1280 cm3.
Volume of 10 cones with hemispherical tops = Volume of the cylindrical container
20r3 = 1280
r3 = 64 => r = 4 cm
Hence radius of the ice-cream cone is 4 cm.
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