A circular pond has a radius of 13m. A path goes all the way round
the circumference of the pond. The path is 1-2 m wide throughout.
Find the area of the path.
Is that one-half (1/2) meter wide?
3.14765
Yeh it's 1.2
To find the area of the path around the pond, we need to subtract the area of the inner circle (pond) from the area of the outer circle (path). Here are the steps to calculate it:
1. Calculate the radius of the inner circle, which is the radius of the pond minus the width of the path: 13m - 1m = 12m.
2. Calculate the area of the inner circle using the formula A = πr^2, where A is the area and r is the radius:
A_inner = π * (12m)^2
3. Calculate the area of the outer circle using the formula A = πr^2, where A is the area and r is the radius:
A_outer = π * (13m)^2
4. Finally, calculate the area of the path by subtracting the area of the inner circle from the area of the outer circle:
A_path = A_outer - A_inner
Now, let's calculate the area of the path:
A_inner = π * (12m)^2
= π * 144m^2
≈ 452.39m^2
A_outer = π * (13m)^2
= π * 169m^2
≈ 530.66m^2
A_path = A_outer - A_inner
= 530.66m^2 - 452.39m^2
≈ 78.27m^2
Therefore, the area of the path around the pond is approximately 78.27 square meters.