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
In a corner of the park is a quarter-circle flower bed with a radius of 100 m.
The keeper puts a railing all the way round it.
(Take π as 3.14.)
How long is the railing altogether, in m?
Show the hints (2)
💡Hint 1: What makes up the edge all the way round? Besides the curved arc, what else is there?
💡Hint 2: The arc is a quarter of the whole circumference, and circumference = 3.14 × diameter. Don't forget the two straight edges.
Worked solution
Have a go first, then read the solution step by step.
1.The curved part is a quarter of the whole circumference: 3.14 × 200 ÷ 4 = 157 m.
2.There are also two straight edges, both radii: 100 × 2 = 200 m.
3.Perimeter = 157 + 200 = 357 m.
⚠️Common mistake: counting only the curved part (157 m), or adding just one radius. Both straight edges of the quarter circle are on its perimeter.
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