If the radius of a sphere is measured as 7 m with an error or 0.02 m, find the approximate error in calculating its volume.

Explanation

Suppose radius and volume of the sphere be `x` and `y` respectively.

Here `y=4/3pix^3`

`x=7`

` trianglex=0.02m`

`implies x+trianglex=7.02m`

As`y=4/3pix^3`,

`implies {dy}/{dx}=4pix^2`

`implies( {dy}/{dx})_{x=7}=196pi`

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