Question

Check dimensional correctness of the following relation.
Volume of sphere=4/3πr^2

Answer 1

its not correct dimensionally as the dimensions on the left are L^3 while that on right are L^2.
so it should be 4/3 πr^3.
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Answer 2

Explanation:

The expression of the given relation is as follows;

Volume of sphere=4/3πr^2

The dimension of the sphere is $L^{3}$.

The dimension of the square of the radius is $L^{2}$.

It is concluded from the given relation that the volume of the sphere is not equal to the square of the radius. Here, L.H.S is not equal to R.H.S.

The given relation is not dimensional correct. It should be Volume of sphere=4/3πr^3. It is dimensional correct formula.

The dimension of the sphere is $L^{3}$.

The dimension of the cube of the radius is $L^{3}$.

Here, L.H.S is equal to R.H.S.