Question

Suppose a central angle is inscribed inside of a circle. The angle measures 36 degrees and the minor arc is 15 cm. Calculate the area of the circle and round your answer to two decimal places.

Answer 1

The area of the circle is 1790.49 centimeters square

To calculate the area of the circle, we shall need the radius of the circle

We can get the radius from the arc length

Mathematically, the length of an arc is;

`\frac{\theta}{360\text{ }}\text{ }*\text{ 2}\pi r`

From the question, the length is 15 cm while the central angle is 36

Thus we have;

`\begin{gathered} 15\text{ = }(36)/(360)\text{ }*\text{ 2}\pi r \\ \\ 150\text{ = 2}\pi r \\ \\ \pi r\text{ = 75} \\ \\ r\text{ = }(75)/(\pi) \end{gathered}`

Mathematically, the area of the circle will be;

`\begin{gathered} A\text{ =}\pi\text{ }* r^{2^{}} \\ \\ A\text{ = }\pi\text{ }*\text{ }(75)/(\pi)\text{ }*\text{ }(75)/(\pi) \\ \\ A\text{ = }(75^2)/(\pi)\text{ = 1,790.49 cm} \end{gathered}`