Question

Find the area of the sector of a circle of radius 10 m with a central angle ofTa4Round the solution to two decimal places.

Answer 1

Let's list down the given data in the question.

radius = 10 meters

central angle = 7π/4

The formula in getting the area of the sector given radius and central angle in radian is:

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

Since we have the value of the radius and angle in radian already, let's plug it in to the formula above. Use π = 3.14159

$A=(3.14159)(10m)^2\times\frac{\frac{7\pi}{4}}{2\pi}$

Then, solve.

$\begin{gathered} A=3.14159\times100m^2\times\frac{7}{8} \\ A=274.889125m^2 \\ A\approx274.89m^2 \end{gathered}$

Hence, the area of the sector of circle given radius and angle is approximately 274.89 square meters.