cylinder in a sphere

[red and white kop!]

a cylinder is cut from a solid sphere of radius 3cm. given that the cylinder has height 2h, find its radius in terms of h. hence show that the volume V cubic centimetres of the cylinder is given by
V = 2 x pi x h (9 - h^2)
now this has me stuck bcos i would have tried to find a relation between r and h by using the formula for V. but since this is ruled out, i really have no idea where to start.

 

[Deleted member 4993]

a cylinder is cut from a solid sphere of radius 3cm. given that the cylinder has height 2h, find its radius in terms of h. hence show that the volume V cubic centimetres of the cylinder is given by
V = 2 x pi x h (9 - h^2)
now this has me stuck bcos i would have tried to find a relation between r and h by using the formula for V. but since this is ruled out, i really have no idea where to start.

Draw a sketch of the problem.

Draw a circle with center at O - to represent the sphere.

Draw a rectangle ABCD inside the circle (symmetrically around O) - to represent the cylinder. Let AB be at the bottom (= CD at the top) - representing the diameter of the cylinder and the height is BC (= AD).

Now drop a perpendicular OP from O onto AB. Join OB.

OB = 3 = radius of the sphere

OP = h = half height of the cylinder

PB = 1/2 AB = radius of the cylinder = ?(OB[sup:2nyeq5kq]2[/sup:2nyeq5kq] - OP[sup:2nyeq5kq]2[/sup:2nyeq5kq])

and continue....