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Question

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball of radius 9 cm is dropped into the tub and thus the level of water is raised by h cm. What is the value of h ?


Solution

The radius of the cylindrical tub is 12cm. Upon dropping a spherical ball of radius 9cm into the tub, the height of the raised water is hcm. Therefore, the volume of the raised water is

V=π×122×h cm3

The volume of the spherical ball is

V1=43π×(9)3 cm3

Since, the volume of the raised water is same as the volume of the spherical ball, we have

V1=V

43π×93=π×122×h

h=4×933×122

h=274=6.75 cm

Therefore, the height of the raised water is
H = ​​​​6.75 cm


Mathematics
RD Sharma
Standard X

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