TS EAMCET · Maths · Application of Derivatives
The diameter of a sphere is measured as \(42 \mathrm{~cm}\). If there is an error of \(1 / 77 \mathrm{~cm}\) in measuring it, then the error involved in the volume of that sphere (in cubic centimeters) is
- A 33
- B \(\frac{24}{7}\)
- C 36
- D \(\frac{36}{7}\)
Answer & Solution
Correct Answer
(C) 36
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} d=42 \mathrm{~cm} ; r=21 \mathrm{~cm} \\ & V=\frac{4}{3} \pi r^3 \text { and } \Delta V=\left(\frac{d}{d r} v\right) \times \Delta r \\ & \Rightarrow \Delta V=\frac{d}{d r}\left(\frac{4}{3} \pi r^3\right) \Delta r \Rightarrow \Delta V=\left(\frac{4}{3}…
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