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16 September, 13:04

A circle has a radius of 6 centimeters. What is the area of the sector formed by a central angle measuring 2.4 radians? Enter your answer, as a decimal, in the box.

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  1. 16 September, 14:43
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    Area of a circle can be calculated using the following formula

    Area = πr²

    where π = 3.14 and r - radius of circle

    Area of the whole circle is for a central angle of 360°.

    We are asked to find the area of a sector. Sector is when 2 arms enclose a central angle by which one arm has rotated.

    1 radian = 57.3°

    2.4 radian = 57.3 x 2 = 137.52°

    Area for 360° = πr²

    area for 137.52° = πr² / 360° x 137.52 = π x 6 cm x 6 cm x 0.382 = 13.752 cm²
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