The measure of central angle RST is pi radians. What is the area of the shaded sector?

Solution:

Given, the measure of central angle is pi radians.

We have to find the area of the shaded sector.

We know, a central angle of pi radians subtends an area of semicircle.

The area of semicircle is given by the formula,

\(A=\frac{1}{2}\pi r^{2}\)

From the figure,

Radius, r = 4 units.

Now, \(A=\frac{1}{2}\pi (4)^{2}\)

\(A=\frac{1}{2}\pi (16)\)

\(A=8\pi\) square units.

Therefore, the area of the shaded sector is 8\pi\) square units.

The measure of central angle RST is pi radians. What is the area of the shaded sector?

Summary:

The measure of central angle RST is pi radians. The area of the shaded sector is 8\pi\) square units.