Question

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Answer 1

A cylindrical tub of radius = 12cm

Depth = 20cm

Let r cm be the radius of the ball

Then, the volume of the ball = the volume of water raised

=`4/3πr^3 = π r^2h`

=`4/3πr^3 = π xx(12)^2 xx6.75`

⇒  `r^3=(144xx6.75xx3)/4`

⇒ `r^3=729`

⇒  r = 9cm

Thus, radius of the ball = 9cm.