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 = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
In this equation [tex]\pi[/tex] is a dimensionless quantity, and the unit of v is [tex]m^{3}[/tex].
But, metre is a measure of length, thus it has a dimension of L.
So that,
[tex]m^{3}[/tex] ≅ [tex]L^{3}[/tex]
Then,
[tex]L^{3}[/tex] = [tex]r^{3}[/tex]
Find the cube root of both sides to have,
r = L
Therefore, the dimension of the radius of a sphere is L.
