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Question

A solid consisting of a right circular cone of height 120cm and radius 60cm standing on a hemisphere of radius 60cm is placed upright in a right circular cylinder full of water such that it touches the bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is 60cm and its height is 180cm.

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Solution

Water left in cylinder=Volume of cylinder-volume of hemisphere-volume of cone
Water left=πr2h23πr313πr2h
Water left=π×602×18023π×60313π×602×120
Vremaining=1130973.355cm3

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