The area of a sector with a central angle of 45° and a diameter of 5.6 in. is 1.23 square inches.
To see why, you can use the formula for the area of a sector, which is:
A = (θ/360) x π x r^2
where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.
First, you need to find the radius of the sector, which is half of the diameter:
r = d/2 = 5.6/2 = 2.8 in.
Next, you can plug in the values for θ and r into the formula:
A = (45/360) x 3.14 x 2.8^2 = 1.23 square inches
Therefore, the area of the sector is 1.23 square inches.
The area of a sector with a central angle of 120° and a radius of 18.4 m is 1908.57 square meters.
To see why, you can use the same formula for the area of a sector:
A = (θ/360) x π x r^2
First, you need to convert the radius from meters to centimeters, since π is in terms of centimeters:
r = 18.4 m x 100 cm/m = 1840 cm
Next, you can plug in the values for θ and r into the formula:
A = (120/360) x 3.14 x 1840^2 = 1908.57 square meters
Therefore, the area of the sector is 1908.57 square meters.