Please Read Through This, Answers are Listed.
As a heads up, this post is going to be very long.
So to do these questions, first know what you need to do.
Goals to do:
1 - Find the area of the circle
2 -Find how much of it is shaded
3 -Find the shaded's area.
So, the first goal is to find the area of the circle, well that's fairly simple. Just do pi r². (r stands for the radius)
With the first question, they list the length GH as 11 inches. So just plug it in!
pi 11² ---> pi * 121 ---> ≈380.13
Next, find the amount that is shaded. So with that, look at the angle inside the circle, it is 64°. By knowing that the whole circle is 360°, just do 64/360 to find the an "important number".
64/360 ---> 0.17777777...
By using this important number and multiplying it with your total circle area, you'll get your answer.
380.13 * 0.17777777... ---> ≈ 67.6in² (QUESTION 1 ANSWER)
And then just do the same with the rest...
Question 2:
pi 22² ---> pi * 484 ---> 1520.53
139/360 ---> 0.38611
1520.53 * 0.38611 ---> ≈ 587.09cm² (QUESTION 2 ANSWER)
Question 3:
pi 3² ---> pi * 9 ---> 28.27
84/360 ---> 0.2333...
28.27 * 0.2333 ---> ≈6.60mm² (QUESTION 3 ANSWER)
Question 4:
pi 14.2² ---> pi * 201.64 ---> 633.47
***Because the angle is in the blank space, subtract it from 360 first before continuing.
360 - 87 ---> 273/360 ---> 0.7583333
633.47 * 0.7583333 ---> ≈480.38m² (QUESTION 4 ANSWER)
Question 5:
pi 9² ---> pi * 81 ---> 254.47
***Because the angle is in the blank space, subtract it from 360 first before continuing.
360 - 42 ---> 318/360 ---> 0.88333
254.47 * 0.88333 ---> ≈224.78in² (QUESTION 5 ANSWER)
Question 6:
pi 28² ---> pi * 784 ---> 2463.01
115/360 ---> 0.319444
2463.01 * 0.319444 ---> ≈786.79m² (QUESTION 6 ANSWER)
Question 7:
pi 32.5² ---> pi * 1056.25 ---> 3318.31
29/360 ---> 0.080555
3318.31 * 0.080555 ---> ≈267.31ft² (QUESTION 7 ANSWER)
Question 8
pi 29.5² ---> pi *870.25 ---> 2733.97
***Because the angle is in the blank space, subtract it from 360 first before continuing. Along with that, the angle has a square in place of a number, meaning that it is a right angle, or 90°.
360-60 ---> 270/360 ---> 0.75
2733.97 * 0.75 ---> 2050.48mi² (QUESTION 8 ANSWER)
Okay, that's all!