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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?

 

My answer--> 300(pi symbol) mm^2

Am I right?

Guest May 31, 2017

Best Answer 

 #2
avatar+2117 
+1

First, know the formula of a sector;

 

Let r= radius

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!
   

 

Therefore, your answer is correct!

TheXSquaredFactor  May 31, 2017
 #1
avatar+87293 
+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

 

 

 

cool cool cool

CPhill  May 31, 2017
 #2
avatar+2117 
+1
Best Answer

First, know the formula of a sector;

 

Let r= radius

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!
   

 

Therefore, your answer is correct!

TheXSquaredFactor  May 31, 2017

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