Question

A central angle of a circle is 90 degrees. If the diameter of the circle is 12 cm, what is the area of segment created by connecting two points on the circle created by the angle described? Round your answer to the nearest hundredth

Answer 1

Answer:

$A=28.26\ cm^2$

Step-by-step explanation:

we know that

If the central angle of the circle is 90 degrees, then the sector will have an area equal to one quarter of the whole circle.

so

$A=\frac{1}{4}\pi r^{2}$

we have

$r=12/2=6\ cm$ ----> the radius is half the diameter

$\pi =3.14$

substitute

$A=\frac{1}{4}(3.14)(6)^{2}$

$A=28.26\ cm^2$

Answer 2

The area of a segment created by connecting two points on the circle created by the angle described is 28.26 $cm^2$.

Calculation of the area of the segment:

Since A central angle of a circle is 90 degrees. If the diameter of the circle is 12 cm

So here the area should be

$= 1\div 4 \pi r^2\\\\= 1\div 4 (3.14) (6)^2$

= 28.26 $cm^2$

hence, The area of a segment created by connecting two points on the circle created by the angle described is 28.26 $cm^2$.

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