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 .

Answer 1

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