Question

cylindrical bucket with base radius 15 centimetre is filled with water up to a height of 20 centimetre . a heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water . find increase in the level of water

Answer 1

volume of water displaced = volume of spherical ball
πr^2h = (4/3)πR^3
225h = (4/3)729
225h = 972
h = 4.32 cm

hence the increase in level of water is 4.32 cm

Answer 2

Answer:

4.32 cm

Step-by-step explanation:

Given :A cylindrical bucket with base radius 15 centimeter is filled with water up to a height of 20 centimeter .

A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water .

To Find :  find increase in the level of water

Solution:

Radius of cylinder = 15 cm

Let height of the water in the cylinder after a heavy iron sphere is dropped in bucket be h

So, Volume of water displace from cylindrical bucket = $\pi r^2 h$

                                                                                   = $\pi (15)^2 h$

Radius of sphere = 9 cm

Volume of sphere = $\frac{4}{3} \pi r^3$

                           = $\frac{4}{3} \pi (9)^3$                                                                              

So, Volume of water displaced = Volume of sphere

So,  $\pi (15)^2 h=\frac{4}{3} \pi (9)^3$

$(15)^2 h=\frac{4}{3} \times (9)^3$

$h=\frac{4}{3 \times 15^2} \times (9)^3$

$h=4.32 cm$

Hence increase in the level of water is 4.32 cm