Question
A sphere,cylinder,and cone are of the same radius and same height. Find the ratio of their curved surface area.
Answers
Steve
since the height of a sphere is the diameter, the cone and cylinder have height 2r. The areas are thus
sphere: 4πr^2
cylinder: 2πr^2 + 2πrh = 6πr^2
cone: πr^2 + √5πr^2
sphere:cylinder:cone = 4:6:(1+√5)
sphere: 4πr^2
cylinder: 2πr^2 + 2πrh = 6πr^2
cone: πr^2 + √5πr^2
sphere:cylinder:cone = 4:6:(1+√5)