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