Question

A metallic sphere of radius 21 cm is dropped into a cylindrical vessel, which is partly, filled with water. The diameter of the vessel is 1.68 m. If the sphere is completely submerged, find by how much the surface of water will rise.

Answer 1

Radius of the sphere, r = 21 cm
Volume of the sphere `= ((4)/(3)pir^(3)) cm^(3)`
`= ((4)/(3) pi xx 21 xx 21 xx 21) cm^(3) = (12348pi) cm^(3)`
Volume of water displaced by the sphere = `(12348pi) cm^(3)`
Suppose that the water rises by h cm. Then,
volume of water displacd = volume of cylinder of radius 84 cm and height h cm
`:. pi xx 84 xx 84 xx h = 12348pi rArr h = ((12348)/(84 xx 84)) = (7)/(4) cm`
`= 1.75 cm`
Hence, the surface of water will rise by 1.75 cm