Question

The measure of central angle QRS is 8pi/9 radians. What is the area of the shaded sector?

Answer 1

The area of the shaded sector must be 144π units².

What is the area of the circle?

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = $\pi r^{2}$

We know that the angle measurement of central angle QRS is less than π radians.

for r = 18 units

The area of the circle = π18² = 324π  units²

The area of ​​the half of a circle = 324π /2 = 162π units²

The area of ​​a quarter of a circle = 324π /4 = 81π  units²

so

The area of the shaded sector < 162π  units²

and

The area of the shaded sector > 81π  units²

Hence the answer must be 144π units²

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