Sphere formula

A perfectly symmetrical 3 – Dimensional circular shaped object is a Sphere. The line that connects from the center to the boundary is called radius of the square. You will find a point equidistant from any point on the surface of a sphere. The longest straight line that passes through the center of the sphere is called the diameter of the sphere. It is twice the length of the radius of the sphere.

Sphere Formula

Sphere Formula

Formulas of a Sphere

There are four main formulas for a sphere which include sphere diameter formula, sphere circumference formula, sphere surface area, and sphere volume area. All these formulas are mentioned in the table given below and an example is also prodided here.

Sphere Formulas
Diameter of a Sphere D = 2 r
Circumference of a Sphere C = 2 π r
Surface Area of a Sphere A = 4 π r3
Volume of a Sphere V = (4 ⁄ 3) π r3

Solved Examples Using Formulas of a Sphere

Question: Calculate the diameter, circumference, surface area and volume of a sphere of radius 9 cm ?

Solution:

Given,

r = 7 cm

Diameter of a sphere
=2r
= 2 × 9
=18 cm

Circumference of a sphere

= 2πr
= 2 × π × 9
= 56.54 cm

Surface area of a sphere

\(4\pi r^{2}\) \(4\times \pi \times 9^{2}\) \(4\times \pi \times 81\) = 1017.87 cm

Volume of a sphere

\(\frac{4}{3}\;\pi r^{3}\) \(\frac{4}{3}\;\pi 9^{3}\) = 338.2722 cm


Practise This Question

In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the