TS EAMCET · Maths · Application of Derivatives
If there is an error of \(\pm 0.04 \mathrm{~cm}\) in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is \(10 \mathrm{~cm}\), is
- A \(\pm 1.2\)
- B \(\pm 0.06\)
- C \(\pm 0.006\)
- D \(\pm 0.6\)
Answer & Solution
Correct Answer
(D) \(\pm 0.6\)
Step-by-step Solution
Detailed explanation
Given, \(\Delta r= \pm \frac{0.04}{2}=0.02\) Volume of sphere \[ V=\frac{4}{3} \pi r^3 \] On differentiating w.r.t. \(r\), we get…
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