Formula for Surface Area of Sphere with Examples

Here you will learn what is the formula for surface area of sphere and examples based on it.

Let’s begin –

What is Sphere ?

A sphere is a three dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the centre of the sphere.

A sphere is like the surface of a ball. The word solid sphere is used for the solid whose surface is a sphere.

Formula for Surface Area of Sphere

Surface Area of Sphere = \(4\pi r^2\)

where r is the radius of sphere.

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

Solution : The surface area of the sphere of radius 7 cm would be

Surface Area = \(4\pi r^2\) = \(4\times {22\over 7} \times 7 \times 7\) = 616 \(cm^2\)

Example : A cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.

Solution : Let radius of cylinder = r.

Diameter of cylinder = 2r

Height of cylinder = \(2\over 3\) (2r) = \(4r\over 3\)

Volume of cylinder = \(\pi r^2 h\) = \(\pi r^2 {(4r\over 3)}\) = \(4\pi r^3\over 3\)

Volume of the sphere with radius 4 cm = \(4\over 3\) \(\pi (4)^3\) = \(4\over 3\) \(\pi (64)\)

According to the question,

Volume of the cylinder = Volume of sphere

\(\implies\)  \(4\over 3\) \(\pi r^3\) = \(4\over 3\) \(\pi (4)^3\)

\(\implies\)  \(r^3\) = \((4)^3\)  \(\implies\)  r = 4 cm

Hence, radius of base of cylinder = 4 cm

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