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Question

A solid consisting of a right circular cone, standing on a hemisphere, is placed upright, in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cm3 (Take π=227)


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Solution

Radius of the cylinder = 3 cm and its height = 6 cm.

Volume of water in the cylinder, when full = [π×(3)2×6]cm3=(54π)cm3

.Volume of solid consisting of cone and hemisphere = (Volume of hemi-sphere) + (Volume of cone)
= [23π×(2)3+13π×(2)2×4]cm3=(32π3)cm3

Volume of water displaced from cylinder = Volume of solid consisting of cone and hemisphere

= (32π3)cm3
Volume of water left in the cylinder after placing the solid into it

= (54π32π3)cm3=(130π3)cm3=(1303×227)cm3=136.19cm3

Hence, the volume of water left in the cylinder to the nearest cm3 is 136 cm3.


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