Answer:
15. 31.42 cm^2
16. 25.73 m^2
17. Fly A
Step-by-step explanation:
15.
The blue shaded region is a sector of a circle. The formula for area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]
Where [tex]\theta[/tex] is the central angle and r is the radius
For the diagram, we have 80° arc and 180° arc as the "white" area. Since the whole circle is 360°, the shaded region arc is 360 - (80+180) = 100°. this is [tex]\theta[/tex] and the radius is 6.
Plugging in it in the formula we get:
Area of shaded region = [tex]\frac{\theta}{360}*\pi r^2\\=\frac{100}{360}*\pi(6)^2\\=31.42[/tex] cm^2
16.
We can say that area of shaded region = area of parallelogram - area of circle
Now,
Area of Parallelogram = b * h
where
b is the base (it is 6+3=9) and h is the height (diameter of the circle is the height = 6)
Area of Parallelogram = 9 * 6 = 54
Area of Circle = πr^2 where r is the radius, which is 6/2=3
Area of Circle = π(3)^2 = 9π
Now,
Area of Shaded Region = 54 - 9π = 25.73 m^2
17.
For the first figure (rectangle) we could let the height be h (since not given). So area of yellow region would be 4h (area of rectangle is base * height)
And area of whole ruler would be 8*h = 8h
So probability of landing in yellow region would be [tex]\frac{4h}{8h}=\frac{1}{2}=0.5[/tex]
For 2nd figure, the yellow region has area of π(2)^2 = 4π ( radius of yellow circle is 2 and area of circle is πr^2)
Area of whole circle is π(4)^2 = 16π
So probability of landing in yellow region would be [tex]\frac{4\pi}{16\pi}=\frac{1}{4}=0.25[/tex]
Hence, Fly A is more likely to land in a yellow region.
