Question

what is the area of a sector of a circle of radius 5 cm and its angle is 96 degree ?​

Answer 1

The area of a sector of a circle is 20.952 $\text{cm}^{2}$.

Step-by-step explanation:

We have to find the area of a sector of a circle of radius 5 cm and its angle is 96 degrees.

Let the radius of the circle be 'r' = 5 cm

As we know that the area of the circle is given by the following formula;

Area of a circle =  $\pi r^{2}$

                          =  $\frac{22}{7} \times 5^{2}$

                          =  78.57 $\text{cm}^{2}$

Now, the area of a sector of a circle is given by the following formula;

      Area of a sector of a circle =  $\frac{n\°}{360\°} \times \text{Area of a circle}$

Here n° = 96° {given in the question}

So, Area of a sector of a circle =  $\frac{96\°}{360\°} \times 78.57$  

                                                   =  20.952 $\text{cm}^{2}$

Hence, the area of a sector of a circle of radius 5 cm and its angle is 96 degrees is 20.952 $\text{cm}^{2}$.