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*(\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*((7\pi)/(4))/(2\pi)`

Then, solve.

`\begin{gathered} A=3.14159*100m^2*(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.