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A semicircle is divided into two circular sectors of which one is 4/5 of the other. The radius of the circle measures 18cm. Calculate the length of the two arcs and the area of ​​the two circular sectors

User Bobomoreno
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1 Answer

19 votes
19 votes

The length of the two arcs and the area of the two circular sectors can be calculated as follows:

Since the semicircle is divided into two circular sectors, each sector has an angle of 180/2 = 90 degrees. Therefore, the smaller circular sector has an angle of 90 * (4/5) = 72 degrees, and the larger circular sector has an angle of 90 - 72 = 18 degrees.

The length of the arc of a circle is equal to the circumference of the circle multiplied by the ratio of the central angle of the arc to 360 degrees. Therefore, the length of the smaller arc is 18 * pi * (72/360) = 8pi cm, and the length of the larger arc is 18 * pi * (18/360) = 2pi cm.

The area of a circular sector is equal to the area of the circle multiplied by the ratio of the central angle of the sector to 360 degrees. Therefore, the area of the smaller circular sector is 18^2 * pi * (72/360) = 288pi cm^2, and the area of the larger circular sector is 18^2 * pi * (18/360) = 72pi cm^2.

Therefore, the length of the two arcs is 8pi cm and 2pi cm, and the area of the two circular sectors is 288pi cm^2 and 72pi cm^2.

User Saret
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