Question

find the area of the sector of a circle of radius 5 cm with a central angle of 240°. round the solution to two decimal places.

Explanation:

Step1: Recall the sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle measure in degrees and $r$ is the radius of the circle.

Step2: Substitute the given values

We are given that $r = 5$ cm and $\theta=240^{\circ}$. Substitute these values into the formula:
$A=\frac{240^{\circ}}{360^{\circ}}\times\pi\times(5)^{2}$

Step3: Simplify the expression

First, simplify $\frac{240^{\circ}}{360^{\circ}}=\frac{2}{3}$. Then, $(5)^{2}=25$. So, $A=\frac{2}{3}\times\pi\times25=\frac{50\pi}{3}$.

Step4: Calculate the numerical value

Using $\pi\approx3.14159$, we have $A=\frac{50\times3.14159}{3}\approx52.36$ $cm^{2}$.

Answer:

$52.36$ $cm^{2}$