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Question

A conical vessel of radius 12cm and depth 16cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the inner curved surface of the vessel, it is just immersed up to the topmost point of the sphere. How much water over flows out of the vessel out of the total volume V cubic units?

A
14V
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B
34V
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C
38V
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D
89V
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Solution

The correct option is D 89V
Diameter of the sphere is equal to the height of the cone =16cm
=> Radius of the sphere =8cm
Volume of a cone =13πr2h
where, r is the radius of the base of the cone and h is the height.
Hence, volume of the given cone,
V=13π×122×16=768π
Volume of sphere =43πr3
Hence, Volume of water displaced = V
olume of the sphere =43×π×83=20483×π
Now, 20483×pi768×π=89
Hence, 89 of the total volume is spilled out.

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