Find the area of the sector determined by the given radius r and central angle θ. Express the answer both in terms of π and as a decimal approximation rounded to two decimal places.
(a) r = 7 cm: θ = π/10
(b) r = 17 m; θ = 5°
(c) r = 21 ft; θ = 11π/6
(d) r = 7.9 in.; θ = 170°
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|dw:1442023375990:dw| This is a sector.
You can think of it as a fraction of the whole circle. For example is the angle is 180degrees the area of the sector is half the area of the entire circle.
Therefore to get the area of the sector you just have to get what proportion of the entire circle it is (using the angle) and times it by the area of the circle
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For question (a) the radius is 7, therefore the area of the circle is pi x r^2 = pi x 7^2
As the angle is pi/10, to find what fraction of the entire circle it is you divide pi/10 by 2pi and 2pi is the whole cirlce.
(pi/10)/2pi = 1/20
Therefore the area of the sector is 1/20 x 49pi = 49/20 pi