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# If the Perimeter of a Sector of a Circle of Radius 6.5 Cm is 29 Cm, Then Its Area is - Mathematics

MCQ

If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is

#### Options

•  58 cm2

• 52 cm2

•  25 cm2

• 56 cm2

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#### Solution

We know that perimeter of a sector of radius l=2r+θ/360xx2pir ...............(1)

We have given perimeter of the sector and radius of the sector and we are asked to find the area of the sector. For that we have to find the sector angle.

Therefore, substituting the corresponding values of perimeter and radius in equation

(1) we get,

29=2xx6.5+θ/360xx2pixx6.5.............(2)

We will simplify equation (2) as shown below,

29=2xx6.5(1+θ/360xxpi)

Dividing both sides of the equation by 2xx6.5, we get,

29/2xx6.5=(1+θ/360xxpi)

Subtracting 1 from both sides of the equation we get,

29/2xx6.5-1=θ/360xxpi.............(3)

We know that area of the sector = θ/360xxpi^2

From equation (3), we get

Area of the sector  = (29/(2xx6.5)-1)r^2

Substituting r=6.5 we get,

Area of the sector =(29/(2xx6.5)-1)6.5^2

Area of the sector=((29xx6.5^2)/(2xx6.5)-6.5^2)

Area of the sector=((29xx6.5)/2-6.5^2)

Area of the sector=(188.5/2-42.25)

Area of the sector=(94.25-42.25)

Area of the sector=52

Therefore, area of the sector is 52 cm^2

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Q 22 | Page 70
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