If the increase in the side of a square is 6 | vedclass

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

Question

(B) Let the side of the square be $x$. Given that the percentage change in the side is $6 \%$,so $\frac{dx}{x} 	imes 100 = 6 \%$. The area of the squ

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) Let the side of the square be $x$. Given that the percentage change in the side is $6 \%$,so $\frac{dx}{x} 	imes 100 = 6 \%$. The area of the square is $A = x^2$. Differentiating with respect to $x$,we get $\frac{dA}{dx} = 2x$,which implies $dA = 2x \, dx$. Dividing both sides by $A = x^2$,we get $\frac{dA}{A} = \frac{2x \, dx}{x^2} = 2 \frac{dx}{x}$. To find the percentage change in area,multiply by $100$: $\frac{dA}{A} 	imes 100 = 2 	imes \left( \frac{dx}{x} 	imes 100 ight)$. Substituting the given value,we get $	ext{Percentage change in Area} = 2 	imes 6 \% = 12 \%$. Thus,the approximate percentage increase in the area is $12 \%$. Therefore,option $B$ is correct.

If the increase in the side of a square is $6 \%$,then the approximate percentage increase in its area is: (in $\%$)

Similar Questions

The approximate value of $(7.995)^{1/3}$ correct to four decimal places is

Electric current $(I)$ is measured by a galvanometer, where the current is proportional to the tangent of the angle $( \theta)$ of deflection. If the deflection is read as $45^{\circ}$ and an error of $1\%$ is made in reading the angle, the percentage error in the current is:

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

If an error of $0.02 \text{ cm}^2$ is found in the surface area of a sphere when its radius is measured as $10 \text{ cm}$, then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is

Find the approximate value of $f(2.01),$ where $f(x)=4x^{2}+5x+2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module