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प्रश्न
In a cylindrical vessel of diameter 24 cm, filled up with sufficient quantity of water, a solid spherical ball of radius 6 cm is completely immersed. Find the increase in height of water level.
उत्तर
Radius of spherical ball r = 6 cm, radius of cylindrical vessel r1 = 12 cm
Since, the ball completely immersed into the vessel, the water level is increased.
Let the height of increased level.
Therefore,
The volume of increase water level = volume of ball
`pi xx (12)^2 xx x = 4/3 pi xx (6)^3`
`144 x = 4/3 xx 216`
`144x = 4 xx 72`
`x = (4 xx 72)/144`
x = 2 cm
Hence, the level of water increased by 2 cm.
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Assertion (A)
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Reason (R)
Volume of a sphere `=4/3pi"R"^3`
Surface area of a sphere = 4πR2
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
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