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Question
A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result, one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged?
Solution
Volume of vessel = Volume of water = `1/3pir^2h`
Diameter = 25.2 cm,
Therefore radius = 12.6 cm
Height = 32 cm
Volume of water in the vessel = `1/3pir^2h`
= `1/3 xx 22/7 xx 12.6 xx 12.6 xx 32`
= 5322.24 cm3
On submerging six equal solid cones into it, one-fourth of the water overflows.
Therefore, volume of the equal solid cones submerged
= Volume of water that overflows
= `1/4 xx 5322.24`
= 1330.56 cm3
Now, volume of each cone submerged
= `1330.56/6`
= 221.76 cm3
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