Question

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

Answer 1

The area of the segment created by connecting the two points on the circle created by the angle described is 28.26 square centimeter

Solution:

Given that,

A central angle of a circle is 90 degrees

diameter of the circle is 12 cm

radius = 12/2 = 6 cm

To find: Area of segment

The area of sector when angle is in degrees is:

$Area\ of\ sector = \frac{\theta}{360} \times \pi r^2$

Where,

r is radius

$\theta$ is angle in degrees

Therefore,

$Area\ of\ sector = \frac{90}{360} \times 3.14 \times 6^2\\\\Area\ of\ sector = 0.25 \times 3.14 \times 36\\\\Area\ of\ sector = 28.26$

Thus area of the segment created by connecting the two points on the circle created by the angle described is 28.26 square centimeter