If the radius of a sphere is measured as 9   cm with an error of 0 . 03   cm , then find the…

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.
  1. 2.16πcm2
  2. 21.6πcm2
  3. 216πcm2
  4. 0.216πcm2

Solution

Let r be the radius of sphere & ∆r be the error in measuring the radius.

Then r=9 & ∆r=0.03

Now, the surface area of sphere is given by, S=4πr2

⇒∆S=8πr∆r

⇒∆S=8π×9×0.03=2.16π cm2

Asked in: AP EAMCET 2021 (20 Aug Shift 1)

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