Question

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The radius of a sphere is measured to be 6 inches, with a possible error of...

The radius of a sphere is measured to be 6 inches, with a possible error of 0.02 inch. Using differentiation, approximate the maximum possible error in calculating the volume of the sphere.

Expert Solution

As given radius of a sphere is measured to be 6 inches with a possible error of 0.02 inch we have to find the maximum possible error in calculating the volume of the sphere using differentiation

we know that volume of a sphere with radius r is given by,

Differentiate both the side with respect to r we can say that,

As given radius of a sphere is measured to be 6 inches, with a possible error of 0.02 inch hence we can say that,

r = 6 and dr = 0.02 and we can write,

Hence we can say that maximum possible error in calculating the volume of the sphere 2.88pi

we can also write,

rounding to two decimal places

Hence we can say that maximum possible error in calculating the volume of the sphere is 9.05

milcah answered 2 years ago

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