Question

If the area of minor sector of a circle with radius 11.2cm is 49.28cm^2find the measure of the arc

Answer 1

If the area of minor sector of a circle = 49.28 cm² and radius = 11.2 cm then the measure of the arc is 45°.

Step-by-step explanation:

The radius of the circle, r = 11.2 cm

The area of the minor sector = 49.28 cm²

We know that the formula for the area of the minor sector is given as,

Area of the sector = [θ/360°] * πr² ….. [where θ = measure of the arc]

Now, by substituting the given values in the formula, we get

49.28 = [θ/360°] *  $\frac{22}{7} * (11.2)^2}$

⇒ [θ/360°] = $\frac{49.28}{\frac{22}{7} * (11.2)^2}$

⇒ [θ/360°] = 0.125

⇒ θ = 45°

Thus, the measure of the arc is 45°.

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