The circumference of the base of the cylindrical vessel is 154 cm and its height is 49 mm. How many litres of water can it hold? (correct to three places of decimals, use π = 22⁄7)
- (a)2.439
- (b)9.244
- (c)4.329
- (d)3.924
Answer
Why
Correct — B. Radius from the circumference, height into the same unit, then cubic centimetres into litres.
2πr = 154 → r = 154 × 7 ⁄ (2 × 22) = 24.5 cm
h = 49 mm = 4.9 cm
V = πr²h = (22⁄7) × 24.5 × 24.5 × 4.9
24.5 × 24.5 = 600.25
600.25 × 4.9 = 2941.225
2941.225 × 22 ⁄ 7 = 9243.85 cm³
1 litre = 1000 cm³, so V = 9.24385 L = 9.244 L to three decimals → option (b).
Why the others are wrong
- (a)2.439 — 2.439 L means 2439 cm³. The circumference fixes r at 24.5 cm and the height at 4.9 cm, and 24.5² × 4.9 × 22⁄7 is 9243.85 cm³ — nowhere near it.
- (c)4.329 — 4.329 L means 4329 cm³, under half the true volume. Options (a), (c) and (d) are the same four digits 2, 3, 4 and 9 shuffled, so only the arithmetic separates them — and it returns 9243.85 cm³.
- (d)3.924 — 3.924 L means 3924 cm³. The one quantity the working produces is 9243.85 cm³, which is 9.24385 L and rounds to 9.244.
Concept
Three separate skills are being tested inside one formula.
Circumference to radius. 2πr = 154 with π = 22⁄7 gives r = 154 × 7 ⁄ 44 = 24.5 cm, the 7 and the 22 cancelling cleanly.
Millimetres to centimetres. The height is printed in mm while the radius comes out in cm. 49 mm = 4.9 cm, and skipping the conversion multiplies the answer by ten.
Cubic centimetres to litres. 1 litre = 1000 cm³, so 9243.85 cm³ is 9.24385 L, which is why the question asks for three decimal places.
A shortcut avoids squaring 24.5 altogether. Since r = C ⁄ 2π, the volume is V = C²h ⁄ 4π.
That gives 154² × 4.9 × 7 ⁄ (4 × 22) = 9243.85 cm³ — the same number with the circumference used directly.
Key facts
- The volume of a cylinder is πr²h.
- With π = 22⁄7, a base circumference of 154 cm gives a radius of 24.5 cm.
- 1 litre = 1000 cm³ = 1000 millilitres.
- 10 mm = 1 cm, so a height of 49 mm is 4.9 cm and not 49 cm.
Study next
Common traps
- Leaving the height as 49 cm, which returns 92.44 L instead of 9.244 L
- Treating 154 cm as the radius or the diameter rather than the circumference
- Dividing 9243.85 cm³ by 100 instead of 1000 when converting to litres
The two measurements arrive in different units and one of them is a circumference rather than a radius, so the first two lines of work are conversion, not mensuration.
Cylinders where a surface measure has to be turned into the missing dimension are also asked at 19 Sep 2024, 12:30, Quant Q.13 (curved surface 792 cm², find the volume) and at 13 Sep 2024, 16:00, Quant Q.2 (curved surface 880 cm², find h × r).
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