Question

A cylindrical jar of radius 10 cm is filled with water upto a height of 15 cm. 14 spherical balls
of radius 3 cm each are immersed in the jar. Find the new level to which water is filled in the
Jar​

Answer 1

Answer:

The new level to which water is filled in the jar is 14.73 cm

Step-by-step explanation:

Given as :

A cylindrical jar is filled with water and spherical ball is immersed in it

The radius of cylindrical jar = r = 10 cm

The height water filled in cylindrical jar = h = 15 cm

The radius of spherical ball = r' = 3 cm

Let The new height of water filled in jar = H

According to question

volume of cylinder = v = π × r² × h

Or,  v = 3.14 × (10 cm)² × 15 cm

Or,  v = 4740 cubic cm

so, volume of water up to h height filled in cylindrical jar = v = 4740 cubic cm

Again

volume of spherical ball = v' = $\dfrac{4}{3}$  × π × r'³

i.e  v' = $\dfrac{4}{3}$  × 3.14 × (3 cm)³

Or, v' = 113.04 cubic cm

Now,

Raised water inside jar = volume of water up to h height filled in cylindrical jar - volume of spherical ball

i.e  Raise water inside jar = v - v'

Or, Raised water inside jar = 4740 cm³  - 113.04  cm³

∴   Raised water inside jar = 4626.96 cubic cm

So, That much raise water inside jar raise up to height H with same base radius

So, volume of water raise = π × r² × H

Or, π × r² × H = 4626.96 cm³

Or, 3.14 × 10² × H = 4626.96 cm³

Or, H = $\dfrac{4626.96}{314}$

∴   H = 14.73 cm

So, Height of water displace = H = 14.73 cm

Hence, The new level to which water is filled in the jar is 14.73 cm Answer