there is a water reservoir beneath a circular garden to supply a foutain in the garden.the reservoir has a 26-inch diameter.the garden has a 12-foot diameter. how much of the garden does not contain the waer reservoir?
hello will someone plz help me
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To find out how much of the garden does not contain the water reservoir, we first need to find the area of the garden and the area of the reservoir.
1. Area of the garden:
The diameter of the garden is given as 12 feet, so the radius (half of the diameter) would be 12 / 2 = 6 feet.
To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius. Plugging in the values, we get A_garden = π * (6 feet)^2.
2. Area of the reservoir:
The diameter of the reservoir is given as 26 inches, and we need to convert it to feet since the garden measurements are in feet. There are 12 inches in a foot, so the diameter in feet would be 26 / 12 = 2.17 feet (rounded to 2 decimal places).
Similarly, the radius of the reservoir would be 2.17 / 2 = 1.08 feet (rounded to 2 decimal places).
Using the same formula as above, we get A_reservoir = π * (1.08 feet)^2.
3. Difference in areas:
To calculate the portion of the garden that does not contain the water reservoir, we subtract the area of the reservoir from the area of the garden.
Difference = A_garden - A_reservoir
Now, let's calculate the values.
A_garden = π * (6 feet)^2 = 113.1 square feet (rounded to 1 decimal place)
A_reservoir = π * (1.08 feet)^2 = 3.67 square feet (rounded to 2 decimal places)
Difference = 113.1 square feet - 3.67 square feet = 109.43 square feet (rounded to 2 decimal places)
So, approximately 109.43 square feet of the garden does not contain the water reservoir.