Question

17. There is water to a height of 16 cm in a cylindrical glass jar of radius 12-5 cm. Inside the
water, there is a sphere of diameter 15 cm, completely immersed. By what height will water
go down, when the sphere is removed ?
​

Answer 1

By Archimede's Principle,

Volume of water went down = Volume of sphere

Therefore,

πRcylinder2h=34πRsphere3

12.5×12.5×h=34×215×215×215

On solving,

h=518cm

Answer 2

Answer:

VOLUME OF CYLINDER=22/7×R×R×H

= 22/7×12.5×12.5×H

=3437.5/7

VOLUME OF SPHERE= 4/3 ×22/7×R×R×R

=4/3×22/7×7.5×7.5×7.5

=37125/21

DECREASE IN WATER LEVEL=

VOLUME OF CYLINDER= VOLUME OF SPHERE

3437.5×H/7 = 37125/21

3437.5×H =37125/21×7

3437.5×H=37125/3

H = 37125/3×3437

H = 37125/10312.10312.5

H =3.6CM