Mr. Cruz, a coach of a basketball team, wants to repaint a certain spot in his basketball court. The picture below shows the area in his court called the key. What is the area of the key that needs repainting given that the radius of the circle is 6 ft? Copy and answer in your Math notebook. Ho Key 15 fit Ө r=6 ft Follow the steps discussed in the lesson. Use π = 3.14 What is asked: What are the given: How are you going to solve the problem? Translate the problem into a number sentence. Answer:
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Answer:
What is asked:
What is the area of the key that needs repainting?
What are the given:
The radius of the circle is 6 ft
The angle of the key is 15 degrees
How to solve the problem:
1. Find the area of the entire circle with radius 6 ft using the formula A = πr^2, where r = 6 ft and π = 3.14.
A = πr^2
A = 3.14 x 6^2
A = 113.04 sq. ft
2. Find the area of the sector of the circle that corresponds to the key using the formula A = (θ/360)πr^2, where θ = 15 degrees, r = 6 ft, and π = 3.14.
A = (θ/360)πr^2
A = (15/360) x 3.14 x 6^2
A = 4.71 sq. ft
3. Subtract the area of the sector from the area of the entire circle to get the area of the key that needs repainting.
Area of key = Area of circle - Area of sector
Area of key = 113.04 - 4.71
Area of key = 108.33 sq. ft
Therefore, the area of the key that needs repainting is 108.33 square feet.
Step-by-step explanation:
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