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# Am I right?

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The sector of a circle with a 60 mm radius has a central angle measure of 30.

What is the exact area of the sector in terms of π?

Am I right?

Guest May 31, 2017

#2
+1493
+1

First, know the formula of a sector;

Let m= measure of central angle in degrees

$$A_{sector}=\pi r^2*\frac{m^{\circ}}{360^{\circ}}$$

Now, let's substitute into this formula. 60mm is the radius, and the central angle is also given, 30 degrees:

 $$A_{sector}=\pi (60)^2*\frac{30^{\circ}}{360^{\circ}}$$ Here is the formula again but with the substituted values. Let's simplify $$\pi (60)^2$$ first $$A_{sector}=\frac{3600\pi}{1}*\frac{30^{\circ}}{360}$$ 3600 and 360 can be simplified nicely $$A_{sector}=\frac{10\pi}{1}*\frac{30^{\circ}}{1}$$ Multiply the fractions and leave the answer in terms of pi--like the directions specify! $$A_{sector}=300\pi\hspace{1mm}mm^2\approx942.4777962\hspace{1mm}mm^2$$ Of course, remember units!

TheXSquaredFactor  May 31, 2017
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#1
+79853
+1

Correct  !!!!

The area   =  (1/2)(radius)^2 * ( radian measure of the central angle)  =

(1/2) (60^2) *(pi / 6)   =

(1/2) (3600) * (pi/6)  =

3600pi / 12

300pi  mm^2

CPhill  May 31, 2017
#2
+1493
+1

First, know the formula of a sector;

Let m= measure of central angle in degrees

$$A_{sector}=\pi r^2*\frac{m^{\circ}}{360^{\circ}}$$

Now, let's substitute into this formula. 60mm is the radius, and the central angle is also given, 30 degrees:

 $$A_{sector}=\pi (60)^2*\frac{30^{\circ}}{360^{\circ}}$$ Here is the formula again but with the substituted values. Let's simplify $$\pi (60)^2$$ first $$A_{sector}=\frac{3600\pi}{1}*\frac{30^{\circ}}{360}$$ 3600 and 360 can be simplified nicely $$A_{sector}=\frac{10\pi}{1}*\frac{30^{\circ}}{1}$$ Multiply the fractions and leave the answer in terms of pi--like the directions specify! $$A_{sector}=300\pi\hspace{1mm}mm^2\approx942.4777962\hspace{1mm}mm^2$$ Of course, remember units!