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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 - Mathematics

MCQ

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

Options

  • \[\frac{2}{9}\] cm

  • \[\frac{4}{9}\]cm

  • \[\frac{9}{4}\] cm

  • \[\frac{9}{2}\]cm

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Solution

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`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 24 | Page 89
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