Final answer:
To find out how much fertilizer John will need to cover the circular garden with a diameter of 17.5 feet, we first calculate the area of the garden using the formula A = πr², where r is the radius. Then, we use the given ratio to determine the amount of fertilizer needed based on the area of the garden.
Step-by-step explanation:
To find out how much fertilizer John will need to cover the circular garden, we first need to calculate the area of the garden.
The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius.
Since we are given the diameter, we can find the radius by dividing it by 2.
So, the radius of the garden is 17.5 feet / 2 = 8.75 feet.
Now, we can calculate the area of the garden using the formula: A = π(8.75)².
Plugging in the values, we get A ≈ (3.14)(8.75)² ≈ 240.97 square feet.
Now, we can determine how much fertilizer John will need by using the given ratio of 3 teaspoons of fertilizer for every 30 square feet of garden.
Since the garden is 240.97 square feet, we can set up a proportion:
3 teaspoons / 30 square feet = x teaspoons / 240.97 square feet.
Cross-multiplying and solving for x, we get x ≈ (3 teaspoons)(240.97 square feet) / 30 square feet ≈ 24.097 teaspoons of fertilizer.
Therefore, John will need approximately 24.097 teaspoons of fertilizer to cover the garden.