Sphere formula

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 Solid

\[\large Diameter\;of\;a\;sphere=2r\]

\[\large Circumference\;of\;a\;sphere=2\pi r\]

\[\large Surface\;area\;of\;a\;sphere=4\pi r^{2}\]

\[\large Volume;of\;a\;sphere=\frac{4}{3}\: \pi r^{3}\]

Solved Example

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 each of the following question, an Assertion (A) is followed by a corresponding Reason (R). Use the following keys to choose the appropriate answer: 

Assertion (A): There is a natural asymmetry between converting work to heat and converting heat to work. 
Reason (R): No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.