a worker in a city park needs to cover a circular path around the outside of a flower garden with gravel. the radius of the garden is 15 feet and the path surrounding the garden is 6 feet wide. how many square feet need to be covered with gravel? explain how you arrived at your answer.
i had the same math project but your going to have to do this by yourself or you will never learn about area correctly
To figure out the area that needs to be covered with gravel, we need to calculate the area of the outer circle and subtract the area of the inner circle.
Step 1: Calculate the area of the outer circle:
The radius of the garden is given as 15 feet. Since the path surrounds the garden, we need to consider the radius of the path as well. The outer circle would have a radius equal to the sum of the radius of the garden and the width of the path.
Radius of the outer circle = Radius of the garden + Width of the path
= 15 feet + 6 feet
= 21 feet
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the values:
Area of the outer circle = π × (21)^2 square feet
Step 2: Calculate the area of the inner circle:
The inner circle represents the garden, so its radius is given as 15 feet. Using the same formula as above:
Area of the inner circle = π × (15)^2 square feet
Step 3: Subtract the area of the inner circle from the area of the outer circle to find the area of the gravel path:
Area of the gravel path = Area of the outer circle - Area of the inner circle
Now, you can calculate the final answer by subtracting the area of the inner circle from the area of the outer circle.