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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 of the cylinder is 60cm and its height is 180 cm.

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1133400 {cm}^{3}

1130400 {cm}^{3}

1135400 {cm}^{3}

1138400 {cm}^{3}

answer is B.

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Detailed Solution

Given,
Cone radius r= 60 cm
Cone height h= 120 cm
Hemisphere radius= 60 cm
Cylinder radius= 60 cm
Cylinder height= 180 cm
Question Image

Thus, the volume of cone can be given as,,

= \frac{1}{3} π r^{2} h

= \frac{1}{3} π \times 660^{2} \times 120

= 14000 π {cm}^{3}

Also, volume of hemisphere,

= \frac{4}{3} π r^{3}

= \frac{2}{3} π 60^{3}

= 144000 π {cm}^{3}

Volume of cylinder,

= π r^{2} h

= π \times 60^{2} \times 180

= 648000 π {cm}^{3}

Inside the cylinder remaining water,

= π r^{2} h - \frac{1}{3} π r^{2} h - \frac{4}{3} π r^{3} h

= (648000 - 288000) π

= 360000 π

= 1130400 {cm}^{3}

Correct option is 2.

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