Topics › Circles › Q136
Circle · area from circumference
P6 · Circles · PSLE Maths
Hint
First use the circumference formula C = 2πr to find the radius, then use the same radius in the area formula A = πr².
Show the answer and step-by-step explanation
Answer: Area of the mat 616 cm²
- Read the circumference — The question gives the distance around the edge of the circle, which is the circumference. It is not the area, so we cannot use the area formula straight away.
- Find the radius first — The circumference formula is C = 2πr. To find the area, the key is to first find the radius r.
- Substitute to find r — Substitute C = 88 and π = 22/7. Work backwards to find the radius.
- Then find the area — Now that we have the radius, use the area formula: A = πr². Notice: this is the same radius found from the circumference.
- Calculate the answer — Cancel first: 14 ÷ 7 = 2. So the area = 22 × 2 × 14 = 616 cm². 📌 Key idea: when the circumference is given, find the radius using C = 2πr first, then use the same r in A = πr².
Method: When the circumference is given, find the radius r using C = 2πr. The circumference and area share the same radius, so then use A = πr² to find the area.
Practice: 3 similar questions
- Raju has a circular coaster. The length around its edge is 44 cm. Take π = 22/7. Find the area of the coaster.
Answer
154 cm² — The circumference C = 44 cm, and C = 2πr. r = 44 ÷ (2 × 22/7) = 7 cm. Area A = 22/7 × 7 × 7 = 154 cm².
- Mei Ling made a circular class badge. She used 110 cm of ribbon to go exactly once around the badge. Take π = 22/7. Find the area of the badge.
Answer
962.5 cm² — The circumference C = 110 cm. r = 110 ÷ (2 × 22/7) = 17.5 cm. Area A = 22/7 × 17.5 × 17.5 = 962.5 cm².
- At the Science Club, a small robot moves 3 rounds along a circular track and travels 264 cm in total. Take π = 22/7. Find the area enclosed by the circular track.
Answer
616 cm² — 3 rounds are 264 cm, so the circumference for 1 round is C = 264 ÷ 3 = 88 cm. r = 88 ÷ (2 × 22/7) = 14 cm. Area A = 22/7 × 14 × 14 = 616 cm².
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