Question

The area of this circle is 72π m².

What is the area of a 45º sector of this circle?

8π m²

9π m²

12π m²

18π m²

Answer 1

The area of the sector will be 9π m².

We know, area of circle is given as πr², where r is the radius of the circle.
Here Area of circle,C = 72π m²

Area of a sector that subtends an angle 45° at the center (the area shaded in yellow color) is given as:

    A = 72$\pi m^{2}$×$\frac{45}{360}$
⇒ A = 45× $\frac{1}{5}$π m².
⇒ A = 9π m².