From a circle with the radius of 15.75 cm, a sector with the arc length of 11 cm is cut off. Find the area (in cm²) of this sector.

Correct option is B

Given:

Radius of circle = 15.75 cm

Length of an arc = 11 cm

Formula Used:

Length of arc = $$\frac{2\pi r \theta}{360}$$​​

Area of sector = $$\frac{\pi r^2 \theta}{360}$$​​

Solution:

Putting the values in the formula, we get

Length of arc = $$\frac{2 \times \frac{22}{7} \times 15.75 \times \theta}{360}$$​​

11 $$\times$$​ 360 = 44 $$\times$$​ 2.25 $$\times \theta$$​​

​$$\theta=\frac {3960}{99}=40$$​​

So, Area of sector = ​$$\frac{\frac{22}{7} \times 15.75 \times 15.75 \times 40}{360}$$​​

Area of sector = $$\frac {31185}{360}=86.625$$​​