Which of the following could be used to calculate the area of the sector in the circle shown above?

Question

anonymous · Answer

attachment

anonymous · Answer

@mathstudent55

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

To find the area of a sector of a circle, start withe formula for the area of a circle.

For a circle:

$\Large A = \pi r^2$

A sector of a circle is a portion of circle, and the sector's area is proportional to the central angle that intercepts the circle, so the area of the sector is the same fraction of the circle's area as the central angle of the sector is to the entire circle.

If a central angle measures n degrees, then that angle is n/360 of the entire central angle of 360 degrees.

The area of the sector is the same fraction of the entire are of the circle:

$\Large A_{sector} = \dfrac{n}{360^o} \pi r^2$

mathstudent55 · Answer

In your case, n = 37 deg, and r = 10 in.

anonymous · Answer

Which of the following could be used to calculate the area of the sector in the circle shown above?

 π(10in)237 over 360
 π(10in)37 over 360
 π(37in)210 over 360
 π(37in)10 over 360

mathstudent55 · Answer

$\Large A_{sector} = \dfrac{n}{360^o} \pi r^2$

$\Large A_{sector} = \dfrac{37^o}{360^o} \pi (10~in.)^2$