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AP EAMCET202120 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

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.

Options

  1. A2 . 16 π cm 2
  2. B21 . 6 π cm 2
  3. C216 π cm 2
  4. D0 . 216 π cm 2

Correct answer

A. 2 . 16 π cm 2

Step-by-step 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 = 4 π r 2 ⇒ ∆ S = 8 π r ∆ r ⇒ ∆ S = 8 π × 9 × 0 . 03 = 2 . 16 π   cm 2

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