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प्रश्न
A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by
पर्याय
\[\frac{2}{9}\] cm
\[\frac{4}{9}\]cm
\[\frac{9}{4}\] cm
\[\frac{9}{2}\]cm
उत्तर
The radius of sphere, r = 3 cm
The volume of sphere
\[= \frac{4}{3} \pi r^3 \]
\[ = \frac{4}{3}\pi \left( 3 \right)^3 \]
\[ = 36\pi {cm}^3\]
Since,
The sphere fully immersed into the vessel, the level of water be raised by x cm.
Then,
The volume of raised water = volume of sphere
`pi(4)^2 xx x = 36pi`
`x = 36/16`
`x = 9/4 cm`
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