# cylinder in a sphere

• Jun 22nd 2009, 11:59 PM
furor celtica
cylinder in a sphere
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.
• Jun 23rd 2009, 12:12 AM
pickslides
pretty hard to explain this one without a diagram to point at

$\displaystyle r = \sqrt{3^2-h^2}$

Is taken from a right angled triangle where the long side (3 units) is from the middle to the point where the top of the cylinder meets the sphere. The 2 shorter sides are half of the height of the cylinder (h) and the remaining small side is the radius of the sphere.
• Jun 23rd 2009, 12:19 AM
furor celtica
thanks i have a diagram but i didnt feel the need to attach it, i'll figure it out with what you said.