Surface Area of a Sphere Formula

Surface Area of a Sphere Formula

Surface Area of a Sphere

A sphere is a three-dimensional (3D) shape which has a curved surface. It has no edges and no corners. The area occupied by its curved surface is called the surface area of a sphere. The examples of sphere include football, basketball, soccer ball, globe, etc.

Let us study to find the formula to calculate the surface area of a sphere.

We can find the formula to calculate the surface area of a sphere using the formula to calculate the surface area of a cylinder.

Let us take a sphere and a cylinder with the same radius and the same height.

If the radius of the sphere is r, then the height of the cylinder, h = 2r as shown in the above figure.

Suppose we made this cylinder with a paper, then this cylinder is open from top and bottom. If we open up the cylinder and cover up the sphere with the paper obtained after opening it, then we see that the paper covers the whole surface of the sphere. It means that the curved surface area of the cylinder is equal to the surface area of sphere.

Hence, the surface area of the sphere = Curved surface area of the cylinder

                                                                    = 2πrh

Here, the height of the cylinder, h = 2r

Thus, the surface area of the sphere = 2πr(2r) = 4πr2

Surface area of a sphere = 4πr2

 

Surface Area of a Sphere Formula

Surface area of a sphere = 4πr2


Surface Area of a Sphere Example


Example 1: Find the surface area of a sphere whose radius is 7 cm.

Solution: Given: r = 7 cm

Surface area of a sphere = 4πr2

                                             = 4 × 22/7 × 7 × 7

                                              = 616 sq. cm

 

Example 2: How much material is required to make a football of radius 14 cm.

Solution: Given: r = 14 cm

Surface area of a sphere = 4πr2

                                             = 4 × 22/7 × 14 × 14

                                              = 2464 sq. cm

 

Example 3: If the surface area of a globe is 9856 sq. cm, find the diameter of the globe.

Solution: Given: Surface area = 9856 sq. cm

Surface area of a sphere = 4πr2

                                   9856 = 4 × 22/7 × r2

                                         r2 = 68992/88 = 784

                                          r = 28 cm

Diameter = 2r = 2 × 28 = 56 cm

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