Question

What is the area of a sector with a central angle of 2π/9 radians and a diameter of 20.6 mm? use 3.14 for π and round your answer to the nearest hundredth. enter your answer as a decimal in the box.
this is just to help people:)

Answer 1

Answer:

37.03 sq. mm.

Step-by-step explanation:

A sector is "part" of a circle. The formula for area of a sector (in radians) is:

Area of sector = $\frac{1}{2}r^2 \theta$

Where

r is the radius (half of diameter)

$\theta$  is the central angle of the sector

In this problem, the diameter is given as 20.6, so radius would be:

Radius (r) = 20.6/2 = 10.3

The central angle is given as  $\frac{2\pi}{9}$ radians

Now, we substitute and find the value for the area:

$A=\frac{1}{2}r^2 \theta\\A=\frac{1}{2}(10.3)^2 (\frac{2\pi}{9})\\A=\frac{1}{2}(106.09)(\frac{2(3.14)}{9})\\A=53.045*0.698\\A=37.03$

Thus,

Area of sector = 37.03 sq. mm.