AP EAMCET · Maths · Application of Derivatives
If the radius of a sphere is mentioned as \(7 \mathrm{~m}\) with an error of \(0.02 \mathrm{~m}\), then the approximate error in calculating its volume is
- A \(1.83 \pi \mathrm{m}^3\)
- B \(2.25 \pi \mathrm{m}^3\)
- C \(4.39 \pi \mathrm{m}^3\)
- D \(3.92 \pi \mathrm{m}^3\)
Answer & Solution
Correct Answer
(D) \(3.92 \pi \mathrm{m}^3\)
Step-by-step Solution
Detailed explanation
Radius \((r)=7 \mathrm{~m}\) Error in radius \((d r)=0.02 \mathrm{~m}\) Volume of sphere \((v)=\frac{4}{3} \pi r^3\) differentiate w.r. to ' \(r\) ' on both sides,…
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