Question

If the area of a sector of a circle is $\frac{5}{18}$ of the area of the circle, then the sector angle is equal to
(a)60°
(b)90°
(c)100°
(d)120°

Answer 1

Answer:

The sector angle of a circle is 100°.

Among the given options option (c) 100°  is the correct answer.

Step-by-step explanation:

Given :

Area of a sector of a circle is 5/18 the area of the circle.

Area of a sector of a circle = 5/18 × area of the circle.

θ/360 × πr² = 5/18 × πr²

θ/360 = 5/18  

18θ = 360 × 5

θ = (360 × 5)/18

θ = 20 × 5  

θ = 100°  

Sector angle of a circle = 100°

Hence, the sector angle of a circle is 100°.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:

Let radius of the circle= r

Sector angle = x°

_______________________

i) Area of the circle = πr²

ii) Area of the sector =

(x/360)×πr²

_______________________

According to the problem given,

Area of the sector = (5/18) × Area of the circle

=> (x/360)×πr² = (5/18)×πr²

=> x/360 = 5/18

=> x = (5×360)/18

=> x = 5 × 20

=> x = 100°

Therefore,

Option (C) is correct.

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