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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 bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

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Solution


Volume of water left in cylinder = Volume of cylinder Volume of solid

Volume of cylinder:

Radius, r=60 cm

Height, h=180 cm

Volume of outer cylinder = πr2h=227×602×180=142560007

Volume of solid= Volume of cone + Volume of hemisphere

Volume of cone:

Radius, r=60 cm

Height,h=120 cm

Volume of cone = 13πr2h

=13×227×602×120

=31680007cm3

Volume of hemisphere:
radius, r=60 cm
Volume = 23πr3

=23×227×603

=31680007

Volume of solid =31680007+31680007=63360007

Now, Volume of water left in cylinder = Volume of cylinder - Volume of solid

=14256000763360007

=79200007 cm3
=1131428.57 cm3
=1131428.57×1100×1100×1100m3 [Since, 1 cm=1100 m]
=1.131 m3


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