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Question
A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball is dropped into the tube and the level of the water is raised by 6.75cm.Find the radius of the ball .
Solution
Given that radius of a cylindrical tube (r) =12cm
Level of water raised in tube(h)= 6.75cm
Volume of cylinder = πr2h
= π (12)2 x 6.75cm3
=`22/7(12)^2 6.25cm^3` ..........(1)
Let ‘r’ be radius of a spherical ball
Volume of sphere=`4/3pir^3` ...........(2)
To find radius of spherical balls
Equating (1) and (2)
=`pixx(12)^2xx6.75=4/3pir^3`
`r^3=(pixx(12)^2xx6.75)/(4/3xxpi)`
r3 = 729
r3 = 93
r = 9cm
∴Radius of spherical ball(r) = 9cm
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