A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160 $c m^{2}$ and its height 12 cm, determine the radius of any of the spheres.

Open in App

Solution

Area of the base of the cuboid = 160 cm²
Let the radius of the sphere be r cm.
Volume of three spheres $= 4 π r^{3}$ [3 times volume of single sphere]
Increased height of the cuboidal vessel = 2 cm
Increased volume of the water $= 160 \times 2 = 320 c m^{3}$
Since the volume is increased after immersing the 3 spheres in the vessel, increased volume of water will be equal to the volume of three spheres.

$=> 4 π r^{3} = 320$

$=> r^{3} = 25.45$

$=> r = 2.94 c m$

Thus, the radius of the spheres is 2.94 cm.

Suggest Corrections

Similar questions

Q. A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by

2 c m

. If the area of the base of the cuboid is

160 {c m}^{2}

and its height

12 c m

, determine the radius of any of the spheres.

A vessel is in the shape of cuboid and contains some water,if three identical spheres are immersed then the water level increases by 2 cm.If the area of the base of the cuboid is 160cm² and height is 12cm then find the radio of the sphere.

Q. A cylindrical vessel of radius

4 c m

contains water. a solid sphere of radius

3 c m

is lowered the water until it is completely immersed. The water level in the vessel will rise by

Q. A cylindrical vessel of radius

4 c m

contains water. A solid sphere of radius

3 c m

is lowered into the water, until it is completely immersed. Find the rise in the water level ( in

c m

) in the vessel.

Q. A cube of

9 c m

edge is immersed completely in a rectangular vessel containing water. If the dimension of the base are

15 c m

and

12 c m

, find the rise in water level in the vessel.

Join BYJU'S Learning Program

A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160 cm2 and its height 12 cm, determine the radius of any of the spheres.

A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160 $c m^{2}$ and its height 12 cm, determine the radius of any of the spheres.