A circular garden has a diameter of 28 m. If a gardener wants to fence 75% of the garden's circumference, what length of fencing is needed? (Use π= 22⁄7)
- (a)56 m
- (b)66 m
- (c)64 m
- (d)62 m
Answer
Why
Correct — B. Find the full circumference, then take three-quarters of it.
Circumference = π × d
Multiply: 22⁄7 × 28 = 22 × 4 = 88 m
75% = 3⁄4, so fencing = 3⁄4 × 88
Multiply: 3 × 22 = 66 m → option (b)
Why the others are wrong
- (a)56 m — 56 m is 7⁄11 of the 88 m circumference, about 63.6%. Working back, 56 ÷ 0.75 ≈ 74.7 m, not the garden's 88 m.
- (c)64 m — 64 m is 8⁄11 of 88 m, about 72.7%, not 75%. Working back, 64 ÷ 0.75 ≈ 85.3 m, short of the true 88 m circumference.
- (d)62 m — 62 m is 31⁄44 of 88 m, about 70.5%, which is 4 m short of the three-quarters the gardener wants.
Concept
Circumference = πd = 2πr. With π = 22⁄7 and a diameter that is a multiple of 7, the 7 cancels at once: 28 ÷ 7 = 4, so C = 22 × 4 = 88 m.
A percentage of a boundary is that fraction of its length. 75% = 3⁄4, and 88 divides by 4, so the answer comes out whole.
Fencing 75% of the boundary means fencing an arc that subtends 270° at the centre, since 0.75 × 360° = 270°. Arc length = 270⁄360 × 88 gives the same 66 m.
Key facts
- Circumference = πd = 2πr.
- With π = 22⁄7, a 28 m diameter gives a circumference of 88 m.
- Arc length = θ⁄360° × 2πr, so 75% of a circle is a 270° arc.
Study next
Common traps
- Treating 28 m as the radius, which doubles the circumference to 176 m and the fence to 132 m.
- Computing the area πr² = 616 m² instead of the boundary length.
Circumference also decides 15 Sep 2025, 16:00, Quant Q.20, worked backwards: ₹3,768 at ₹120 per metre is 31.4 m, so 2πr = 31.4 and r = 5 m.
25 Sep 2024, 12:30, Quant Q.15 adds two circumferences: 2π × 12 + 2π × 16 = π × 56, a diameter of 56 cm.
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