WBJEE · Maths · Application of Derivatives
If the radius of a spherical balloon increases by \(0.1 \%\), then its volume increases approximately by
- A \(0.2 \%\)
- B \(0.3 \%\)
- C \(0.4 \%\)
- D \(0.05 \%\)
Answer & Solution
Correct Answer
(B) \(0.3 \%\)
Step-by-step Solution
Detailed explanation
Let \(V\) be the volume of spherical ballon of radius \(r\) Then, \(V=\frac{4}{3} \pi r^{3}\) \(\Rightarrow \quad \log V=\log \left(\frac{4 \pi}{3}\right)+3 \log r \Rightarrow \frac{1}{V} \frac{d V}{d r}=0+\frac{3}{r}\)…
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