If the percentage error in the radius of a ci | vedclass

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

Question

(A) Let $r$ be the radius and $A$ be the area of the circle.Given that the percentage error in the radius is $\frac{dr}{r} 	imes 100 = 3\%$,so $\frac

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Let $r$ be the radius and $A$ be the area of the circle.Given that the percentage error in the radius is $\frac{dr}{r} 	imes 100 = 3\%$,so $\frac{dr}{r} = 0.03$.The area of the circle is $A = \pi r^2$.Differentiating with respect to $r$,we get $dA = 2\pi r dr$.The relative error in the area is $\frac{dA}{A} = \frac{2\pi r dr}{\pi r^2} = 2 \frac{dr}{r}$.Substituting the value of $\frac{dr}{r}$,we get $\frac{dA}{A} = 2 	imes 0.03 = 0.06$.Therefore,the percentage error in the area is $\frac{dA}{A} 	imes 100 = 0.06 	imes 100 = 6\%$.

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

Similar Questions

The radius of a sphere is $7 \text{ cm}$. If an error of $0.08 \text{ cm}^2$ is made in measuring its surface area, then the approximate error (in $\text{cm}^3$) found in its volume is:

The approximate value of $(66)^{\frac{1}{3}}$ is

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

Find the approximate value of $\sqrt{25.3}$.

The approximate value of $f(x)=x^3+5x^2-7x+9$ at $x=1.1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module