Question

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 1

Ans : (B)
Hint \(: v=\frac{4}{3} \pi r^{3}, \because \Delta r=\left(\frac{0.1}{100}\right) r \quad \therefore \Delta v=\left(\frac{d v}{d r}\right) \Delta r=4 \pi r^{2} \cdot\left(\frac{0.1}{100}\right) r=\left(\frac{0.3}{100}\right) v\)