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AP EAMCET202018 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

If the radius of a sphere is mentioned as (7 ~m ) with an error of (0.02 ~m ), then the approximate error in calculating its volume is

Options

  1. A(1.83 m ^3 )
  2. B(2.25 m ^3 )
  3. C(4.39 m ^3 )
  4. D(3.92 m ^3 )

Correct answer

D. (3.92 m ^3 )

Step-by-step solution

Radius ((r)=7 ~m ) Error in radius ((d r)=0.02 ~m ) Volume of sphere ((v)= 4 3 r^3 ) differentiate w.r. to ' (r ) ' on both sides, ( aligned & d v d r = 4 3 (3 r^2 ) & d v=4 (r^2 ) d r=4 (49) (0.02) & d v=3.92 m^3 aligned ) Hence, option (d) is correct.

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