Surface Area and Volume of a Sphere

A sphere is a solid shape which is completely round like a ball. It has the same curved and total surface area.

Curved or Lateral surface area of a Sphere\mathrm{4\pi r^2}
Total surface area of a Sphere\mathrm{4\pi r^2}
Volume of a Sphere\mathrm{\left(\dfrac{4}{3}\right)\pi r^3}
 R = radius

Surface Area and Volume of a Hemisphere

If we cut the sphere in two parts then is said to be a hemisphere.

Curved or Lateral surface area of a Sphere\mathrm{2\pi r^2}
Total surface area of a Sphere \mathrm{3\pi r^2}
Volume of a Sphere\left(\dfrac{2}{3}\right)\pi\text r^3
 r = radius

Example

If we have a metal piece of cone shape with volume 523.33 cm3 and we mould it in a sphere then what will be the surface area of that sphere?

Solution

Given, volume of cone = 523.33\ \text{cm}^3

Volume of cone = Volume of Sphere

Volume of sphere =100\ \pi\ \text{cm}^3

523.33\ \text{cm}^3=\dfrac{4}{3}\pi r^3

523.33\times\dfrac{3}{4}\times\dfrac{7}{22}=r^3

125=r^3

r=5

Surface area of a sphere =4\pi r^2

=4\times\dfrac{22}{7}\times5\times5

 =314.28\ \text{cm}^2.

Scroll to Top