Question

Hello! I would appreciate the help, and please write step by step solutions. Will mark brainliest. Thanks!

Answer 1

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 = $\frac{\theta}{360}*\pi r^2$

Where  $\theta$ 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  $\theta$ and the radius is 6.

Plugging in it in the formula we get:

Area of shaded region = $\frac{\theta}{360}*\pi r^2\\=\frac{100}{360}*\pi(6)^2\\=31.42$ 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  $\frac{4h}{8h}=\frac{1}{2}=0.5$

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  $\frac{4\pi}{16\pi}=\frac{1}{4}=0.25$

Hence, Fly A is more likely to land in a yellow region.