Area & Volume Of Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, just like a surface of a round ball. A sphere is mathematically defined as the set of points that are all at the same distance from a given point, but in three-dimensional space.

The distance from the center to the edge is called the radius of the ball, and the line that connects two points on the sphere and is twice the length of the radius is called as diameter.

Area and Volume Of Sphere

A sphere is the 3- D shape where curved surface area equals to the total surface area of the figure. The curved surface area is the area in which only the area of the curved part is covered. The formula does not take into account the circular base

Curved Surface Area = 2πr²

The total surface area on the other hand is a combination of the curved area along with the area of the base The formula for the total surface area  and the curved surface area of the sphere is given below

Surface area (TSA) = CSA = 4πr 2

Volume Of Sphere

The volume of the sphere is defined as the number of cubic units needed to fill a sphere.

S.I unit is given cubic meters ( m³)

The derivation is given as:

Volume Of Sphere

\(\small V=Volume\; of \; the \; Sphere\)

\(\small = Sum \; of \; the \; volumes \; of \; all \; pyramids\)

\(\small = \frac{1}{3}A_{1}r+\frac{1}{3}A_{2}r+\frac{1}{3}A_{3}r+….+\frac{1}{3}A_{n}r+\)

\(\small = \frac{1}{3}(Surface \; area \; of \; the \; sphere)\; r\)

\(\small =\frac{1}{3}\times 4 \pi r^{2} \times r\)

\(\small =\frac{4}{3}\pi r^{3}\)

In the above derivation, the sphere in Fig:2 is divided into pyramids, and the volume of the sphere is equal to the volume of all the pyramids as shown in the figure. The total volume is calculated by the summation of the pyramids volumes.

Practise This Question

The only circular part in a cylinder is its base.