What is the area of a sector where n= the measure of the central angle, r=radius, and d=diameter. n=90 degrees, d=18cm
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Ac = 3.14*r^2 = 3.14 * 9^2=254.48cm^2 = Area of the circle.
A sector is a fraction of a circle.
As = (90/360)254.48,
As = (1/4)254.48 = 63.6cm^2.
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To find the area of a sector when you have the measure of the central angle (n) and the diameter (d), you can follow these steps:
1. First, we need to find the radius (r). Since the diameter (d) is given, we can divide it by 2 to obtain the radius. In this case, d = 18 cm, so the radius (r) would be 18 cm / 2 = 9 cm.
2. Next, calculate the fraction of the circle represented by the central angle. The fraction can be found by dividing the central angle (n) by 360 degrees (the total number of degrees in a circle). In this case, n = 90 degrees, so the fraction would be 90 degrees / 360 degrees = 1/4.
3. Now, we can calculate the area of the whole circle using the formula for the area of a circle: A = πr². Substituting the value of the radius (r = 9 cm) into the formula, we get A = π(9 cm)² = 81π cm².
4. Finally, we multiply the area of the whole circle by the fraction of the circle represented by the central angle (1/4) to find the area of the sector. So, the area of the sector would be (1/4) * 81π cm².
Therefore, the area of the sector is (1/4) * 81π cm², which simplifies to 20.25π cm² or approximately 63.64 cm² (rounded to two decimal places).