Question

a game spinner, circle O, is divided into 3 regions as shown. Line RP is a diameter. What's the area of the shaded sector ROS if RP = 8 in and angle POS = 45 degrees

Answer 1

The rule of the area of the sector is

`A=(x)/(360)*\pi\text{ }* r^2`

Where x is the central angle of the sector

r is the radius of the circle

Since the central angle of the sector is < ROS

Since < POS = 45 degrees

Since < ROS and < POS are linear angles, then

< ROS + 45 = 180

Subtract 45 from both sides

Since PR is the diameter of the circle O

Since PR = 8

Since the radius is half the diameter

The radius is 8/2 = 4

The value of x is 135 and the value of r is 4

Substitute them in the rule above

`A=(135)/(360)*\pi\text{ }*(4)^2`

Use pi = 3.14

`\begin{gathered} A=(3)/(8)*3.14*16 \\ A=18.84 \end{gathered}`

Round it to the nearest tenth

A = 18.8 square inches

The answer is H