Find the area of a quadrant of a circle whose circumference is 66 cm.

Step-by-step solution

Idea: Get the radius from the circumference, then take a quarter of πr².

1. 2 × 227 × r = 66 ⇒ r = 66 × 744 = 212 = 10.5 cm.1 mark
2. Area of circle = 227 × 10.5 × 10.5 = 22 × 1.5 × 10.5 = 346.5 cm².1 mark
3. Quadrant = 14 × 346.5 = 86.625 cm² (≈ 86.63 cm²).1 mark

Answer to write in the exam

Common mistakes that cost marks

• Taking 66 ÷ 2 = 33 as the radius.
• Taking a half instead of a quarter of the circle.

How this can come in the exam

Try one yourself

Find the area of a quadrant of a circle whose circumference is 176 cm. (Use π = 227.)

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