Question

36. Check the dimensional correctness of the following relation.
Volume of a sphere = 4/3 (radius)^2
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Answer 1

volume of a sphere =4/3πr^2

L^3=L^2

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.

hope it helps.

Answer 2

Answer:

Apply principle of homogeneity

L.H.S

Dimensions(Volume)=(L³)

R.H.S

Dimensions(4/3πr³)=(L)³

                                  =(L³)

L.H.S=R.H.S

Therefore, the equation is dimensionally correct

Correct equation for volume of a sphere=4/3πr³