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?
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!
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
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!