Answer:
If we have a circle of radius R, the area of the circle is:
A = pi*R^2
And if we have a section of angle θ, the area of the section will be:
A = (θ/360°)*pi*R^2
13) We have a circle of radius R = 2.
We can see that we have a right angle (90°) plus an angle of 45°
Then the total angle of the shaded part is:
θ = 90° + 45° = 135°
Then the area of the shaded part is:
A = (135°/360°)*pi*2^2 = 1.5*pi
14) Here we have a diameter equal to 10 units, and we know that the radius is half of the diameter, then:
R = 10/2 = 5
Always when we divide an angle by a straight line that passes through the center, we create two angles of 180°.
In the image, we can see that the angle of the non-shaded section is 72°
Then the angle of the shaded region must be such that:
θ + 72° = 180°
θ = 180° - 72° = 108°
Then the area of the shaded region is:
A = (108°/360°)*pi*(5)^2 = 7.5*pi
15) Here we have a circle with a diameter of 12 units, then the radius is:
R = 12/2 = 6
And we can use the same reasoning than before for the angle of the shaded region.
We can see that the angle of the non-shaded region is 120° is given by:
θ + 120° = 180°
θ = 180° - 120° = 60°
Then the area of the shaded region is:
A = (60°/360°)*pi*6^2 = 6*pi