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Question

# A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, (in m3) if the radius of the cylinder is 60 cm and its height is 180 cm?

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Solution

## In the given question,Volume of water in the cylinder = Volume of cylinder − Volume of SolidGiven:Radius of the base of the cone r1=60 cmHeight of the cone h1=120 cm=2r1Radius of the hemisphere r2=60 cm=r1Height of the cylinder h2=180 cm=3r1Radius of the base of the cylinder r3=60 cm=r1Now,Volume of the solid =23π(r1)3+13π(r1)2(2r1)=23π(60)3+13π(60)2(2×60)=13π(60)3[2+2]=43π(60)3Again,Volume of the cylinder =π(r1)2(3r1)=3π(60)3Therefore,Required volume of water =π(60)3[3−43]=53π(60)3=1130973.35 cm3=1.131m3 (approx.)

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