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, if the radius is 60 cm and its height is 180 cm.
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$1133400 cm^3$
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$1130400 cm^3$
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$1135400 cm^3$
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$1138400 cm^3$
B
Correct answer
Explanation
The volume of the solid is the sum of the cone (1/3 * pi * r^2 * h) and the hemisphere (2/3 * pi * r^3). With r=60 and h=120, the solid volume is 1/3 * pi * 60^2 * 120 + 2/3 * pi * 60^3 = 144000*pi + 144000*pi = 288000*pi. The cylinder volume is pi * r^2 * H = pi * 60^2 * 180 = 648000*pi. The remaining water is (648000 - 288000) * pi = 360000 * 3.14 = 1130400.