Area of a sector of central angle 200^{circ} | vedclass

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

Question

Let the radius of the sector $AOBA$ be $r.$

Given that, Central angle of sector $A O B A=	heta=200^{\circ}$

and area of the sector $A O B A=770

Vedclass · Accepted Answer

$73 \frac{1}{3}$

Vedclass · Answer

Let the radius of the sector $AOBA$ be $r.$

Given that, Central angle of sector $A O B A=	heta=200^{\circ}$

and area of the sector $A O B A=770\, cm ^{2}$

We know that, area of the sector $=\frac{\pi^{2}}{360^{\circ}} 	imes 	heta^{\circ}$

$	herefore$ Area of the sector, $770=\frac{\pi^{2}}{360^{\circ}} 	imes 200$

$\frac{77 	imes 18}{\pi}=r^{2}$

$r^{2}=\frac{77 	imes 18}{22} 	imes 7 \Rightarrow r^{2}=9 	imes 49$

$r=3 	imes 7$

$r=21 \,cm$

So, radius of the sector $A O B A=21 \,cm$.

Now, the length of the correspoding arc of this sector $=$ Central angle $	imes$ Radius $\quad\left[\because 	heta=\frac{l}{r}ight]$

$=200 	imes 21 	imes \frac{\pi}{180^{\circ}} \quad\left[\because 1^{\circ}=\frac{\pi}{180} Right]$

$=\frac{20}{18} 	imes 21 	imes \frac{22}{7}$

$=\frac{220}{3} \,cm =73 \frac{1}{3} \,cm$

Hence, the required length of the corresponding arc is $73 \frac{1}{3}\,cm$.

Area of a sector of central angle $200^{\circ}$ of a circle is $770\, cm ^{2}$. Find the length of the corresponding arc of this sector. (in $cm$)

Similar Questions

The radit of two concentric circles are $23\, cm$ and $16 \,cm .$ Find the area of the circular ring formed by the circles. (in $cm^2$)

The radius of a circular ground is $63\, m$. Find the cost of fencing its boundary at the rate of ₹ $50 / m .$ Find the cost of levelling the ground at the rate of ₹ $40 / m ^{2}$.

In a circle with radius $7\,cm ,$ the perimeter of a minor sector is $\frac{86}{3}\,cm .$ Then, the area of that minor sector is $\ldots \ldots \ldots \ldots cm ^{2}$.

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

The radius of a circular ground is $56\,m.$ A $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40 / m ^{2}$ (in ₹)