If the circumference of a circle and the peri | vedclass

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

Question

(A) Let the radius of the circle be $r$ and the side of the square be $a$.
According to the given condition,the circumference of the circle equals th

Vedclass · Accepted Answer

Area of the circle $>$ Area of the square

Vedclass · Answer

(A) Let the radius of the circle be $r$ and the side of the square be $a$.
According to the given condition,the circumference of the circle equals the perimeter of the square:
$2 \pi r = 4a$
$\pi r = 2a$
$a = \frac{\pi r}{2}$
Now,the area of the circle is $A_1 = \pi r^2$.
The area of the square is $A_2 = a^2 = (\frac{\pi r}{2})^2 = \frac{\pi^2 r^2}{4}$.
Comparing $A_1$ and $A_2$:
$\frac{A_1}{A_2} = \frac{\pi r^2}{\frac{\pi^2 r^2}{4}} = \frac{4}{\pi}$.
Since $\pi \approx 3.14$,$\frac{4}{3.14} > 1$.
Therefore,$A_1 > A_2$,which means the area of the circle is greater than the area of the square.

If the circumference of a circle and the perimeter of a square are equal,then

Similar Questions

The diameter of a circular garden is $210 \,m$. Inside it,all along the boundary,there is a path of uniform width $7 \,m$. Then,the area of the path is $\ldots \ldots \ldots \ldots \,m^2$.

In a circle with radius $10 \, cm$,the area of a minor sector is $75 \, cm^2$. Then,the length of the arc of that sector is $\ldots \, cm$.

In a circle with radius $6 \, cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.

The length of the minute hand of a clock is $10.5 \, cm$. The area of the region swept by it in $20$ minutes is $\ldots \, cm^2$.

Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

Vedclass Test Series

Exam Paper Generator

Online Exam Module