An easy question on circles for P5, with a step-by-step solution, diagrams and the answer. A P6 topic. Shaded shapes made of circles and squares are common in the Hua Xia Cup's P6 qualifying round and finals.
The question
The park has a round pond 38 m across (its diameter).
All the way round it, a ring-shaped path 12 m wide is to be laid.
(Take π as 3.14.)
What is the area of the ring-shaped path, in m²?
Show the hints (2)
💡Hint 1: The path together with the pond make a big circle. What is its radius?
💡Hint 2: Ring area = big circle − small circle. Take the 3.14 out first, then work it out.
Worked solution
Have a go first, then read the solution step by step.
1.The pond's radius = 38 ÷ 2 = 19 m.
2.The big circle's radius = the pond's radius + the path's width = 19 + 12 = 31 m.
3.The path's area = big circle − small circle = 3.14 × 31 × 31 − 3.14 × 19 × 19.
4.Take out the 3.14: 3.14 × (961 − 361) = 3.14 × 600 = 1884 m².
⚠️Common mistake: using the width, 12 m, as a radius (3.14 × 12 × 12), or working out the big circle and forgetting to take away the pond.
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