Calculation of Sphere Surface Area
Table of Contents
Surface Area of a Sphere
A sphere is a 3D object which is shaped like a ball/balloon. It is perfectly symmetrical and all the points on the surface are the same distance (radius) from the center. There are no edges/corners and it has one surface, which can be seen in the diagrams below.
The surface area of a sphere is calculated using the equation below:
The surface area is calculated using the radius of the circle shown on the left.
It is the sum of the total area that envelopes this spherical object, and either the radius or diameter (2 x radius) can be used in the calculations.
Imagine a bubble being blown, as we increase the volume of the sphere, the surface area also increases.
A sphere can be divided into two equal parts which are called are hemisphere that passes through the center.
Formula for Surface area of a sphere= 4πr2 = πd2
Surface Area of a Sphere Example 1
A Sphere has radius of 10 cm. What is the surface area of the Sphere?
Solution:
The surface area of a sphere formula is 4πr2 = πd2
Surface area = (4*π*102) = 1257 cm2
This can also be written as 0.1257 m2 (1257 multiplied by 10-4 to convert from cm2 to m2).
Note – remember to check units when calculating the surface area.
Surface Area of a Sphere Example 2
A sphere has diameter of 215 mm. What is the surface area of the sphere?
Solution:
The surface area of a sphere equation is 4πr2 = πd2
Surface area = (π*2152) = 145,220 mm2
This can also be written as 0.145 m2 (145,220 multiplied by 10-6 to convert from mm2 to m2).
Note – remember to check units when calculating the surface area.