Question

Find the area of a sector that has a central angle of 200 degrees and a diameter of 18 cm Leave your answer in terms of pi

Answer 1

Given the Central Angle:

$\theta=200\text{\degree}$

And the diameter:

$d=18\operatorname{cm}$

You need to use the following formula for calculating the area of a sector of the circle:

$A=\frac{\theta\pi r^2}{360\text{\degree}}$

Where "r" is the radius of the circle and θ is the Central Angle (in degrees).

By definition, the radius is half the diameter. Then:

$r=\frac{18\operatorname{cm}}{2}=9cm$

Then, substituting values into the formula and evaluating, you get:

$A=\frac{(200\text{\degree)}\pi(9cm)^2^{}}{360\text{\degree}}$$A=45\pi\text{ }\operatorname{cm}^2$

Hence, the answer is:

$A=45\pi\text{ }\operatorname{cm}^2$