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Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

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8.75 cm2

6.75 cm2

8.25 cm2

9.00 cm2

answer is A.

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Detailed Solution

Let us draw a diagram for our reference. The diagram will be as follows:-

https://www.vedantu.com/question-sets/b93451b2-8b73-489f-8a50-b48a4edd6c297960779548122931501.png

We have the arc length = l = 3.5 cm and r = 5 cm.
Now, we will use the formula of arc length which is

l = 2 πr \times \frac{θ}{360 °}, θ

where l is the arc length, r is the radius of the circle and is the angle of the sector.
So, putting the values in the formula, we will get the following expression:-

3.5 = 2 \times \frac{22}{7} \times 5 \times \frac{θ}{360 °}

Switching LHS to RHS and vice versa, we will have:-

θ = (\frac{3.5 \times 7 \times 360}{2 \times 5 \times 22}) °

θ = (\frac{441}{11}) ° \dots \dots \dots \dots \dots \dots (

A = \frac{θ}{360} \circ \times π \times r^{2},

Putting the value of r, and the value from (1), we will have:-

A = \frac{(\frac{441}{11}) °}{360 °} \times π \times 5^{2}, A = \frac{441}{11 \times 360} \times \frac{22}{7} \times 25

= 8.75cm2
Hence, the area is 8.75cm2

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