Another type of three-dimensional object is a sphere.

 

Sphere
An object whose surface points are all equidistant from its centre. This distance is called the radius.


A sphere's surface area is derived from the surface area of a right cylinder whose height is the same as the sphere's diameter.

Recall that the formula for area of a cylinder is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«msub»«mi»A«/mi»«mrow»«mi»c«/mi»«mi»y«/mi»«mi»l«/mi»«mi»i«/mi»«mi»n«/mi»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«/mrow»«/msub»«mo»=«/mo»«mn»2«/mn»«mi»§#960;«/mi»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»§#960;«/mi»«mi»h«/mi»«/math», where «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»§#960;«/mi»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/math» is the area of the two circular bases and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»§#960;«/mi»«mi»r«/mi»«mi»h«/mi»«/math»is the area of the lateral face.

The lateral face of the cylinder is a rectangle with a length equal to the circumference of the base of the circle, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»§#960;«/mi»«mi»r«/mi»«/math», and a height, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«/math».

The surface area of the lateral face of a cylinder is equal to the surface area of a sphere whose diameter is the same as the cylinder's height.

It follows that,