In a arcade game, the "monster" is the shaded sector of a circle of radius 1 cm, as shown in the figure. The missing piece (the mouth) has a central angle of 60 degrees. What is the area of the monster in cm^2
5/3pi
5/6 pi
or, showing the reasoning,
(1 - 60/360) * pi * 1^2
To find the area of the shaded sector (the monster), you need to use the formula for the area of a sector.
The formula for the area of a sector is given by:
Area = (θ/360) * π * r^2
Where:
θ is the central angle in degrees
π is a mathematical constant approximately equal to 3.14
r is the radius of the circle
In this case, the central angle is 60 degrees and the radius is 1 cm.
Plugging in the values into the formula:
Area = (60/360) * 3.14 * (1^2)
60/360 simplifies to 1/6.
Area = (1/6) * 3.14 * 1
Now, multiply:
Area = 0.5233 cm^2
Therefore, the area of the monster (shaded sector) is approximately 0.5233 cm^2.