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$\frac{22}{7}$]

Analyze the question: A circular pond has a path of uniform width around it. The path is a ring (annulus), so its area is the difference between the area of the large circle (pond + path) and the area of the pond.

Concept: Area of a circle = πr² Area of path = π(R² − r²), where R is the outer radius and r is the pond's radius.

Solution:

• Pond radius: r = 4 m
• Outer radius: R = 4 + 2.5 = 6.5 m

Area of path = (22/7)(6.5² − 4²) = (22/7)(42.25 − 16) = (22/7)(26.25) = 22 × 3.75 = 82.50 m²

Answer: D, 82.50 m²

Tip: Use the difference of two squares to save time: R² − r² = (R − r)(R + r) = 2.5 × 10.5 = 26.25. Notice that 26.25 ÷ 7 = 3.75, so the calculation simplifies neatly with π = 22/7. Also, a common mistake is to use 2.5 as the outer radius or to forget to add the width to the pond's radius. Always add the path width to get the outer radius.