A circular lawn has a radius of 21 m. A circular flower bed with a diameter of 14 m is placed in the middle of the lawn. (Take π = 227)
- Find the circumference of the lawn.
- Find the area of the circular flower bed.
- Find the area of the lawn that is not covered by the flower bed.
Need a hint?
For (b), the flower bed's diameter is given, so find its radius before using the area formula. For (c), find the whole lawn's area first, then subtract.
Worked answer
- (a) Circumference = 2 × 227 × 21 = 132 m
- (b) Radius of flower bed = 14 ÷ 2 = 7 m
- (b) Area of flower bed = 227 × 7 × 7 = 154 m²
- (c) Area of lawn = 227 × 21 × 21 = 1386 m²
- (c) Area not covered = 1386 − 154 = 1232 m²
Answer: 1232 m²
The mistake this question tests
Habit
Radius and diameter in circles
Pupils often use the diameter 14 m as the radius in the area formula, giving 616 m² for the flower bed and a wrong final answer of 770 m².
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