If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius λ %, then the error in its volume, is

# If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius , then the error in its volume, is

1. A

2. B

3. C

4. D

none of these

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### Solution:

let $r$ be the base radius and $h$ be the height of the

cone. Then, $2r=h.$ Let $V$ be the volume of the cone. Then,

$\begin{array}{l}V=\frac{1}{3}\pi {r}^{2}h=\frac{4\pi {r}^{3}}{3}\\ ⇒\frac{dV}{dr}=4\pi {r}^{2}\\ \therefore \mathrm{\Delta }V=\frac{dV}{dr}\mathrm{\Delta }r\\ ⇒\mathrm{\Delta }V=4\pi {r}^{2}\mathrm{\Delta }r\\ ⇒\frac{\mathrm{\Delta }V}{V}×100=\frac{4\pi {r}^{2}}{4}\pi {r}^{3}×100=3\left(\frac{\mathrm{\Delta }r}{r}×100\right)=3\lambda \end{array}$

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