Topics › Circles › Q137
Annulus · find radius from area
P6 · Circles · PSLE Maths
Question
Siti's school has a circular garden. A concentric circular tiled path surrounds the garden. The radius of the inner garden is 21 m, and the area of the tiled path (shaded ring) is 1078 m². Find the outer radius of the tiled path. Take π = 22/7.
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Hint
Find the area of the inner circle first, then add the area of the ring to get the area of the large circle.
Show the answer and step-by-step explanation
Answer: outer radius 28 m
- See the ring — The shaded part is an annulus. We want the radius of the large circle, so call it R. The inner radius is 21 m.
- Large minus small — Area of the ring is: large circle area − small circle area. So we can think: large circle area = small circle area + ring area.
- Find inner area — The inner radius is 21 m. Area = π × r × r, so the inner circle area is 1386 m².
- Find large area — Large circle area = inner circle area + ring area. That is 1386 + 1078 = 2464 m².
- Get radius² — Large circle area = π × R². Now the large circle area is 2464 m², so R² = 2464 ÷ 22/7 = 784.
- Find outer radius — Since 28 × 28 = 784, R = 28. The outer radius of the tiled path is 28 m. 📌 Key idea: For annulus questions, use “large circle − small circle”. When finding a radius from ring area, first get the large circle area, then divide by π to get radius².
Method: Area of annulus = area of large circle − area of small circle. To find a radius, first find the large circle area, then use area ÷ π to get radius².
Practice: 3 similar questions
- Ali makes a circular coaster. The inner circle has radius 14 cm and the outer circle has radius 21 cm. Find the area of the shaded ring. Take π = 22/7.
Answer
770 cm² — Area of large circle = 22/7 × 21 × 21 = 1386 cm². Area of small circle = 22/7 × 14 × 14 = 616 cm². Area of ring = 1386 − 616 = 770 cm².
- Siti's circular fountain has a concentric walkway around it. The fountain radius is 14 m and the area of the walkway ring is 770 m². Find the outer radius of the walkway. Take π = 22/7.
Answer
21 m — Inner circle area = 22/7 × 14 × 14 = 616 m². Large circle area = 616 + 770 = 1386 m². Outer radius² = 1386 ÷ 22/7 = 441, so the outer radius = 21 m.
- Raju's school has a concentric circular running track. The track is 7 m wide and its ring area is 1386 m². Find the outer radius of the track. Take π = 22/7.
Answer
35 m — Outer radius² − inner radius² = 1386 ÷ 22/7 = 441. Difference of squares: outer radius² − inner radius² = (outer radius − inner radius)(outer radius + inner radius). The track is 7 m wide, so outer radius − inner radius = 7. Outer radius + inner radius = 441 ÷ 7 = 63. Outer radius = (63 + 7) ÷ 2 = 35 m.
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