John wants to put a circular garden in his back yard. The garden has a diameter of 16 feet. He needs to cover the garden with peat moss. Each bag of peat moss can cover 90 square feet. How many bags does he need?: *
Compute the area of the field in square feet and divide the answer by 90. Choose the next highest integer.
To calculate the number of bags of peat moss John needs, we first need to find the area of the circular garden.
The area of a circle can be calculated using the formula: A = π * (r^2), where A is the area and r is the radius.
In this case, the garden has a diameter of 16 feet, so the radius (r) is half of the diameter, which is 16/2 = 8 feet.
Now we can substitute the values into the formula: A = π * (8^2) = π * 64.
Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. The approximation for π is 3.14.
So, the area of the circular garden is approximately 3.14 * 64 = 201.06 square feet.
Now, we need to determine how many bags of peat moss are needed to cover this area. Each bag covers 90 square feet.
To calculate the number of bags needed, we divide the total area of the garden by the area covered by each bag: 201.06 / 90 = 2.23 (rounded to two decimal places).
Since you can't have a fraction of a bag, John would need to purchase 3 bags of peat moss to cover the circular garden.