Questions: Find the area of the sector.

Find the area of the sector.
Transcript text: Find the area of the sector.
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Solution

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Solution Steps

Step 1: Find the radius

The length of the arc is given by the formula: Arc Length = (angle/360) * 2πr, where 'angle' is the central angle and 'r' is the radius.

We are given the arc length as 20.3 cm and the central angle as 110°. We can plug these values into the formula and solve for 'r':

20.3 = (110/360) * 2πr 20.3 = (11/36) * 2πr r = (20.3 * 36) / (11 * 2π) r ≈ 10.54 cm

Step 2: Find the area of the sector

The area of a sector is given by the formula: Area = (angle/360) * πr^2

We know the angle is 110° and we calculated the radius to be approximately 10.54 cm. Plugging these values into the formula:

Area ≈ (110/360) * π * (10.54)^2 Area ≈ (11/36) * π * 111.0916 Area ≈ 106.6 cm²

Final Answer

106.6

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