In a cylindrical milk container, the radius of the base is half of its height, and the inner surface area (curved surface plus base) is 616 sq.cm. Approximately how much milk (in litres) can the container hold? (Use √5 ≈ 2.23 and π = 22/7.)

Introduction / Context:
This question models a milk container as a right circular cylinder. You are given a relationship between radius and height, and the inner surface area consisting of the curved surface plus the base. From this information you must find the capacity of the container, that is, its volume, and then express it in litres.

Given Data / Assumptions:
• Radius r of the container is half of its height h, so r = h / 2 or h = 2r.
• Inner surface area Sinner = 616 sq.cm, including curved surface and base only.
• Curved surface area (CSA) = 2πrh.
• Area of base = πr2.
• Volume V = πr2h.
• Use π = 22/7 and approximate conversions, where 1 litre = 1000 cubic centimetres.

Concept / Approach:
First express the inner surface area in terms of r only using h = 2r. Then solve the resulting equation for r. After finding r, compute h, then the volume in cubic centimetres and finally convert this to litres. The options are approximate values, so slight rounding is acceptable.

Step-by-Step Solution:
Step 1: h = 2r from the given relation between height and radius. Step 2: Inner surface area Sinner = curved area + base area = 2πrh + πr2. Step 3: Substitute h = 2r into Sinner: Sinner = 2πr(2r) + πr2 = 4πr2 + πr2 = 5πr2. Step 4: Given Sinner = 616, so 5πr2 = 616. Step 5: Substitute π = 22/7: 5 × (22/7) × r2 = 616 → (110/7)r2 = 616. Step 6: Solve for r2: r2 = 616 × 7 / 110 = 4312 / 110 = 39.2. Step 7: So r ≈ √39.2 ≈ 6.26 cm (using the given approximations). Step 8: Height h = 2r ≈ 12.52 cm. Step 9: Volume V = πr2h ≈ (22/7) × 39.2 × 12.52. Step 10: First compute 39.2 × 12.52 ≈ 490.9, so V ≈ (22/7) × 490.9 ≈ 22 × 70.13 ≈ 1542.9 cubic centimetres. Step 11: Convert to litres: Vlitres ≈ 1542.9 / 1000 ≈ 1.54 litres, which matches option 1.53 litres most closely.

Verification / Alternative check:
If you round r to 6.25 cm and h to 12.5 cm for easier numbers, recompute inner surface area: Sinner ≈ 2πrh + πr2 ≈ 2 × 22/7 × 6.25 × 12.5 + 22/7 × 6.252, which comes close to 616 sq.cm. This confirms that the approximate radius and height are consistent with the given surface area and thus the volume estimate is reliable.

Why Other Options Are Wrong:
• 1.42 litres and 1.71 litres are noticeably away from the computed 1.54 litres and would require significantly different dimensions.
• 1.82 litres is too large given the fixed surface area and the relation h = 2r.

Common Pitfalls:
A common mistake is to assume inner surface area means only the curved surface, ignoring the base. Another pitfall is forgetting to convert from cubic centimetres to litres at the end. Keep track of which areas and volumes are required and double check unit conversions.

Final Answer:
The container can hold approximately 1.53 litres of milk.