A court is 94ft long by 50ft wide.It contains 3 circles, each with a diameter of 12 ft. Two of the circles are located at the free throw line with "half of each circle shaded" and the third circle is at the center. Within the third shaded circle is another circle (not shaded) with a radius of 2 ft. One gallon of paint will cover 110 sq ft. How many gallons of paint will be needed to paint the shaded regions on the court? Use pi as 3.14. Explain.
you have 2 complete circles of 12' diameter.
Subtract from that area the area of the small circle of radius 2.
Now divide the result by 110
22ft
To find the amount of paint needed to paint the shaded regions on the court, we need to first calculate the area of each shaded region and then sum them up.
1. Let's start by calculating the area of the two shaded circles at the free throw line:
- Since the diameter of each circle is 12 ft, we can determine the radius by dividing the diameter by 2: 12 ft ÷ 2 = 6 ft.
- The formula to calculate the area of a circle is: A = π * r^2, where π is approximately 3.14 and r is the radius.
- Plugging in the values, the area of one shaded circle is: A1 = 3.14 * (6 ft)^2 = 3.14 * 36 ft^2 = 113.04 ft^2.
- Since we have two circles, the total area of the two shaded circles will be: A_total = 2 * A1 = 2 * 113.04 ft^2 = 226.08 ft^2.
2. Next, let's calculate the area of the third shaded circle at the center:
- The diameter of this circle is not given, but we can find it using the court's dimensions.
- Since the court is 94 ft long and 50 ft wide, the diameter of the third shaded circle can be determined as the minimum of these two dimensions: diameter = min(94 ft, 50 ft) = 50 ft.
- The radius of this circle is half of the diameter: radius = 50 ft ÷ 2 = 25 ft.
- The area of the circle is then: A2 = 3.14 * (25 ft)^2 = 3.14 * 625 ft^2 = 1962.5 ft^2.
3. Finally, let's calculate the area of the inner circle (not shaded) within the third shaded circle:
- The radius of this circle is given as 2 ft.
- The area can be calculated similarly: A_inner = 3.14 * (2 ft)^2 = 3.14 * 4 ft^2 = 12.56 ft^2.
4. Now that we have the areas of each shaded region, we can sum them up to find the total area:
- Total_area = A_total + A2 - A_inner = 226.08 ft^2 + 1962.5 ft^2 - 12.56 ft^2 = 2176.02 ft^2.
5. Given that one gallon of paint can cover 110 sq ft, we can find the number of gallons needed:
- Gallons_needed = Total_area ÷ 110 sq ft/gallon = 2176.02 ft^2 ÷ 110 sq ft/gallon = 19.78 gallons (rounded to two decimal places).
Therefore, approximately 19.78 gallons of paint will be needed to paint the shaded regions on the court.