If the perimeter of a circle is equal to that | vedclass

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

Question

Let radius of circle be $r$ and side of a square be a.

According to the given condition,

Perimeter of a circle $=$ Perimeter of a square

$2 \

Vedclass · Accepted Answer

$14: 11$

Vedclass · Answer

Let radius of circle be $r$ and side of a square be a.

According to the given condition,

Perimeter of a circle $=$ Perimeter of a square

$2 \pi r=4 a \Rightarrow a=\frac{\pi r}{2}$ ...............$(i)$

Now, $\frac{	ext { Area of circle }}{	ext { Area of square }}=\frac{\pi r^{2}}{(a)^{2}}=\frac{\pi r^{2}}{\left(\frac{\pi r}{2}ight)^{2}}$ [from Eq. $(i)$]

$=\frac{\pi r^{2}}{\pi^{2} r^{2} / 4}=\frac{4}{\pi}=\frac{4}{22 / 7}=\frac{28}{22}=\frac{14}{11}$

Part $I$	Part $II$
$1.$ Formula to find the length of a minor arc	$a.$ $C=2\pi r$
$2.$ Formula to find the area of a minor sector	$b.$ $A =\pi r^{2}$
$3.$ Formula to find the area of a circle	$c.$ $l=\frac{\pi r \theta}{180}$
$4.$ Formula to find the circumference of a circle	$d.$ $A=\frac{\pi r^{2} \theta}{360}$

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

Similar Questions

The length of the minute hand of a clock is $14 \,cm .$ If the minute hand moves from $1$ to $10$ on the dial, then $\ldots \ldots \ldots \ldots cm ^{2}$ area will be covered.

The closed figure formed by an arc of a circle and the radii through its end points is called .........

$\widehat{ ACB }$ is a minor arc of $\odot( O , 8 \,cm ) .$ If $m \angle AOB =45,$ the length of minor $\widehat{ ACB }$ is $\ldots \ldots \ldots . . cm .$

In $\odot( O , r),$ the length of minor $\widehat{ ACB }$ is one-eighth of the circumference of the circle. Then, the measure of the angle subtended at the centre by that arc is $\ldots \ldots \ldots \ldots$