Question

What is the area of a sector with a central angle of$185$and a diameter of $6.4$?

Answer 1

Find the area:

The central angle is$185$; this means that the sector makes up $\frac{185}{360}$of the total circle.

We will multiply this fraction by the area of the total circle.

The area of a circle is given by $A=\pi r².$

Since the diameter is 6.4, the radius is $\frac{6.4}{2}=3.2:$

$A=3.14(3.2)²=32.1536$

We multiply this by the fraction of the circle the sector represents:

$\frac{185}{360}(32.1536)=16.52$

Hence, the area is $16.52.$