# 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

#### 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?

#### APPEARS IN

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