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 jar​

Answer 1

Answer:

The increased height in water level is 5.04 cm

Step-by-step explanation:

Given as :

The radius of the cylindrical jar = r = 10 cm

The height of water filled inside jar = h = 15 cm

The radius of spherical ball = R = 3 cm

The number of spherical ball dropped inside jar = 14

Let The increased height in water level = H cm

According to question

Since The shape of jar is cylindrical

So, The volume of cylinder = volume of cylindrical jar

Or, volume of cylindrical jar =  π × radius² × height

Or, volume of cylindrical jar = π × r² × H

Or, volume of cylindrical jar = π × 10² × H

Again

Volume of spherical ball = $\dfrac{4}{3}$ × π × radius³

Or, Volume of spherical ball = $\dfrac{4}{3}$ × π × R³

Or, Volume of spherical ball = $\dfrac{4}{3}$ × π × 3³

Since 14 spherical balls are immersed in jar

So,  Volume of 14 spherical ball = $\dfrac{4}{3}$ × π × 27 × 14

According to question

Volume of 14 spherical ball =  volume of cylindrical jar

Or, $\dfrac{4}{3}$ × π × 27 × 14 = π × 100 × H

Or, 4 × 9 × 14 = 100 × H

Or, 504 =  100 × H

∴ H = $\dfrac{504}{100}$

i.e H = $\dfrac{126}{25}$  cm = 5.04 cm

So, The increased height in water level = H = 5.04 cm

Hence, The increased height in water level is 5.04 cm  Answer