A sphere of diameter 6 cm is fropped into a right circular cylindrical vessel, partly filled with water. The diameter of the cyulindrical vessel is 12 cm. If the sphere is completely cubmerged in water, by how much will the level of water rise in the cylindrical vessel ?

Explanation

Radius of the sphere, R = 3 cm.
Volume of the sphere `=4/3piR^(3)=(4/3pixx3^(3))cm^(3)=(36pi)cm^(3).`
Radius of the cylindrical vessel, r = 6 cm.
Let the rise in water level be h.
Increase in volume of water when the sphere is submerged
`=pir^(2)h=(pixx6xx6xxh)cm^(3)=(36pih)cm^(3).`
But this volume must be equal to the volume of the sphere.
`:." "26pih=36pirArrh=1 cm`.