Answer: 0.8
Step-by-step explanation:
Central Angle Calculation:
We’re given that each sector has a central angle of 18 degrees and a diameter of 28 yards.
To find the central angle in radians, we’ll use the formula: [ \theta = \frac{s}{r} ] where:
(s) represents the arc length (which is the circumference of the sector).
(r) is the radius (half of the diameter).
The circumference of the sector is equal to the circumference of the entire circle, which is (88, \text{yards}).
Therefore: [ \theta = \frac{88}{28} = 3.14 , \text{radians} ]
Area of the Shaded Sector:
We’re given that the circle measures 360 degrees (which is equivalent to (2\pi) radians).
The central angle of the shaded sector is (2.4) degrees (which we’ll convert to radians): [ \alpha = 2.4 \times \frac{\pi}{180} ]
Now we can find the area of the shaded sector using the formula: [ \text{Sector Area} = \frac{\alpha \cdot r^2}{2} ]
Let’s calculate the area:
Convert the central angle to radians: [ \alpha = 2.4 \times \frac{\pi}{180} = 0.042 , \text{radians} ]
Calculate the radius:
The diameter is given as (15, \text{yards}), so the radius is half of that: [ r = \frac{15}{2} = 7.5 , \text{yards} ]
Compute the sector area: [ \text{Sector Area} = \frac{0.042 \cdot 7.5^2}{2} = 0.7875 , \text{square yards} ]
Rounded to the nearest tenth, the area of the shaded sector is approximately 0.8 square yards.