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Question

The radius of a sphere is measured to be 20cm with a possible error of 0.02 of acm. The consequent error in the surface of the sphere is


A

10.5sq.cm

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B

5.025sq.cm

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C

10.05sq.cm

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D

None of these

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Solution

The correct option is C

10.05sq.cm


Explanation for the correct answer:

Given,

Radius of the sphere is 20cm, possible error of 0.02cm.

We need to find the consequent error in the surface of the sphere

We know that the surface area of a sphere is,

S=4πr2

Where,

S is the surface area of the sphere

r is the radius of the sphere.

On differentiating the above equation with respect to r

S=8πr(r)

=8π×20×0.02=10.05sq.cm

Hence the error in the surface of the sphere is 10.05sq.cm.


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