If the relative errors in the base radius and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that,the relative error of height is $\frac{\delta h}{h} = 0.02$. The relative error of radius is $\frac{\delta r}{r} = 0.02$. The volume of

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Given that,the relative error of height is $\frac{\delta h}{h} = 0.02$. The relative error of radius is $\frac{\delta r}{r} = 0.02$. The volume of the cone is $V = \frac{1}{3} \pi r^2 h$. Taking the natural logarithm on both sides,we get $\ln V = \ln \left( \frac{1}{3} \pi r^2 h ight)$. $\ln V = \ln \left( \frac{\pi}{3} ight) + 2 \ln r + \ln h$. Differentiating both sides,we get $\frac{\delta V}{V} = 2 \left( \frac{\delta r}{r} ight) + \left( \frac{\delta h}{h} ight)$. Substituting the given values,$\frac{\delta V}{V} = 2(0.02) + 0.02 = 0.04 + 0.02 = 0.06$. The percentage error in volume is $\frac{\delta V}{V} 	imes 100 = 0.06 	imes 100 = 6 \%$. Therefore,the percentage error in the volume is $6$.

If the relative errors in the base radius and the height of a cone are same and equal to $0.02$,then the percentage error in the volume of that cone is

Similar Questions

If $y=2x^3-2x^2+3x-5$,then for $x=2$ and $\Delta x=0.1$,the value of $\Delta y$ is:

The approximate value of $\sqrt[5]{33}$ correct to $4$ decimal places is

If the percentage error in the radius of a circle is $3\%$,then the percentage error in its area is (in $\%$)

The approximate value of $\sin 31^{\circ}$ is

The approximate value of $\cos \left(59^{\circ} 30^{\prime}\right)$ is (given $1^{\circ} = 0.0175^{c}, \sin 60^{\circ} = 0.8660$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module