Question

Find the area of the circle. Use your calculator's value of π. Round your answer to the nearest tenth. A) 27.6 yd2 B) 283.5 yd2 C) 243.3 yd2 D) 289.5 yd2

Answer 1

Answer:

$s \approx 282.20ft^2$

Step-by-step explanation:

A circle is a curve made up of all the points that are the same distance from the center. In this problem, we are asked to find the area of the sector. A sector is a region of a circle between two radii. Suppose you have a central angle $\theta$ degrees, the sector can be found as:

$s=\frac{\theta}{360}\times\pi r^{2}$

We know:

$r=14ft \\ \\ \theta=165^{\circ}$

So:

$s=\frac{165^{\circ}}{360^{\circ}}\times\pi (14^{2}) \\ \\ s=\frac{11}{24}\times (196\pi) \\ \\ s=\frac{539}{6}\pi \approx 282.20ft^2$