The circle in figure has center O- the length of minor arc AB - 5- and m - AOB - 50- Calculate the area of the circle-

251

You visited us 251 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Chord

The circle in...

Question

The circle in figure has center O, the length of minor $a r c A B = 5 π$ and m $∠ A O B = 50^{\circ}$ . Calculate the area of the circle.

25 π

No worries! We‘ve got your back. Try BYJU‘S free classes today!

324 π

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

576 π

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1, 296 π

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $324 π$
Given, $∠$ $A O B$ $=$ $50$ degrees
Length of minor arc $A B$ is $5 π$
Therefore, we get
$\frac{50}{360} = \frac{5 π}{2 π r}$ , where $r$ is radius of circle
$\Rightarrow r = 18$

Area of circle is $π \times 18^{2} = 324 π$

Suggest Corrections

Similar questions

Q. In a circle with center O, central angle

A O B

has a measure of

\frac{5 π}{4}

radians. The area of the sector formed by central angle

A O B

is what fraction of the area of the circle?

Q. In the given figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.
(1) ∠ AOB (2)∠ ACB
(3) arc AB (4) arc ACB.

Q. As shown in the figure above, O is the centre and OA and OB are the radii of the circle of 10 units each. Calculate the length of minor arc AB , if

∠ A O B = \frac{2 π}{5}

In the figure given A, B, C and D are four points on the circumference of a circle with centre O. Arc AB = 2 arc BC and ∠AOB = 108⁰. Calculate and justify your answer.

Q. In figure, circle

O

has diameter

¯ ¯¯¯¯¯¯ ¯ A B

of the length

8

. If smaller circle

P

is tangent to diameter

¯ ¯¯¯¯¯¯ ¯ A B

at point

O

and is also tangent to circle

O

, calculate the approximate area of the shaded region.

Join BYJU'S Learning Program

The circle in figure has center O, the length of minor arcAB=5π and m∠AOB=50∘. Calculate the area of the circle.

The correct option is B 324πGiven, ∠ AOB = 50 degreesLength of minor arc AB is 5π Therefore, we get50360=5π2πr , where r is radius of circle⇒r=18 Area of circle is π×182=324π

The circle in figure has center O, the length of minor $a r c A B = 5 π$ and m $∠ A O B = 50^{\circ}$ . Calculate the area of the circle.

The correct option is B $324 π$
Given, $∠$ $A O B$ $=$ $50$ degrees
Length of minor arc $A B$ is $5 π$
Therefore, we get
$\frac{50}{360} = \frac{5 π}{2 π r}$ , where $r$ is radius of circle
$\Rightarrow r = 18$

Area of circle is $π \times 18^{2} = 324 π$