Question

Dimension of radius of sphere​

Answer 1

Answer:

The dimension is L

Explanation:

Dimension analysis is a method of representing quantities majorly with respect to some fundamental quantities of mass (M), length (L), time (T).

A sphere has a definite volume which relates to its radius by:

V = $\frac{4}{3}$$\pi$$r^{3}$

In this equation $\pi$ is a dimensionless quantity, and the unit of v is $m^{3}$.

But, metre is a measure of length, thus it has a dimension of L.

So that,

$m^{3}$ ≅ $L^{3}$

Then,

$L^{3}$ = $r^{3}$

Find the cube root of both sides to have,

r = L

Therefore, the dimension of the radius of a sphere is L.