Question

A circle with radius 12 mm divided into 20 sectors of equal area. Which is the area of one sector to the nearest tenth?

Answer 1

Answer:  The area of one sector is 22.6 sq. mm.

Step-by-step explanation:  Given that a circle with radius 12 mm divided into 20 sectors of equal area.

We are to find the area of one sector to the nearest tenth.

The AREA of a circle with radius 'r' units is given by

$A=\pi r^2.$

Here, the radius of the circle is

r = 12 mm.

Therefore, the area of the circle will be

$A=\pi r^2=\dfrac{22}{7}\times (12)^2=\dfrac{22\times 144}{7}=452.57~\textup{sq. mm.}$

Since the whole circle is divided into 20 equal sectors.

So, the area of one sector is

$A_s=\dfrac{1}{20}\times 452.57=22.62\sim 22.6~\textup{sq. mm.}$

Thus, the area of one sector is 22.6 sq. mm.

Answer 2

The area of a full circle is  (pi) (radius²)

                                       = (pi) (12 mm)² = 144π mm²

1/20 of that is  (0.05) x (144π mm²)

                   =     7.2π mm² = 22.6 mm² .