PLEASE HELP ASAP! IT'S A TEST

You are making cone-shaped hats for a drama production. The pattern calls for circles with a 20-inch diameter. You are to cut out a sector created by a 60° angle, as shown in the figure.

1. What is the circumference, in inches, of the circular base of the conical hat? Round your answer to the nearest tenth.

2. You want to cover the top of the hat with fabric. What is the surface area, in square inches, that you will cover? (do NOT include the base of the cone) Round to the nearest square inch.

1. 62.8 inches

Step-by-step explanation:

The circumference of any given circle can be found with the equation c = 2pi(r) OR c = pi(d). You are given the diameter, which can help you find the circumference if you multiply it by pi, or 3.14. 20 times 3.14 is 62.8, which is the circumference of said circle.

2. 362.76

Step-by-step explanation:

First, find the surface area of the entire cone. You can do that using the equation: A=πr(r+h2+r2)

In order to fill all variables, you must find the radius and the height. You know that the radius is d/2, so you know that the radius is 10. The height you can find with the given angle. If we know that the top angle is 60 degrees and that the height makes a right triangle with the bottom of the cone, we know that we can use trigonometric functions to figure out the missing angle. I won't bore you with details, but know that the ratio 10/x = tan(60). (the ratio of the radius to the height is equal to tangent of the angle 60). Solve, you know that the height is 5.7735. Now plug the height and the radius into the equation and get 676.92.

Then, subtract the area of the base from the entire surface area. The area of the base is just a circle with a radius of 10, which means the area of the base is 314.16. Now subtract that from 676.92, and you've got the surface area of the top of this conical hat.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

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step-by-step explanation: