A circular pond of radius 4m has a path of width 2.5m round it. Find, correct to two decimal places, the area of the path. [Take\(\frac{22}{7}\)]

Answer Details

To find the area of the path around the circular pond, we need to subtract the area of the inner circle from the area of the outer circle. The radius of the outer circle is the sum of the radius of the pond and the width of the path. Therefore, the radius of the outer circle is: 4m + 2.5m = 6.5m The area of the outer circle is given by: A_outer = π * r_outer^2 A_outer = π * (6.5m)^2 A_outer = 132.73\(m^2\) The area of the inner circle is simply: A_inner = π * r_inner^2 A_inner = π * (4m)^2 A_inner = 50.27\(m^2\) Therefore, the area of the path is: A_path = A_outer - A_inner A_path = 132.73\(m^2\) - 50.27\(m^2\) A_path = 82.46\(m^2\) Rounding to two decimal places, the area of the path is approximately 82.50\(m^2\). Therefore, the correct option is: - 82.50\(m^2\)