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

#2**+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**+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**+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