Spheres and cylinders?

a solid spherical ball of radius 10 cm is dropped into a vertical cylinder containing water and the height of water rises by 10 cm. find the radius of the cylinder.

Assuming the sphere sinks, it displaces water equal to its own volume, which is (4/3)pi*(10 cm)^3. Apparently this is also equal to
pi*(r-cyl)^2*(delta-h) = pi*(r-cyl)^2*(10 cm), and therefore
(4/3)*100 cm^2 = (r-cyl)^2, and the radius of the cylinder is
(10 cm)*sqrt(4/3) = 11.55 cm.

Calculate the volume of the ball. Then solve for the radius of a 10 cm tall calender with that volume.

Hello charese: You have :
--------------------------------------

VBALL = Delta VWCYL

VBALL = ( 4 / 3 ) ( pi ) ( rBALL^3 )

VBALL = ( 4 / 3 ) ( pi ) ( 10^3 ) = 4189 cu cm

Delta VWCYL = ( pi ) ( rCYL^2 ) ( Delta h )

rCYL = SQRT [( VBALL 0 / ( pi ) ( Delta h ) ]

rCYL = SQRT [ ( 4189 ) / ( pi ) ( 10 ) ]

rCYL = SQRT [ 133.33 ]

rCYL = 11.55 cm <----------------------