Scaling a Recipe and a Water Tank
A canteen uses a cylindrical water tank of radius 0.6 m and height 1.5 m. A recipe for 40 servings of soup needs 3.5 litres of stock, and the canteen must make 130 servings. The cook plans to fill the tank, then use a 5-litre jug to carry water to the kitchen. A supplier claims the tank holds "about 1,700 litres". The canteen also needs to know how many full 5-litre jugs can be drawn from a full tank, and whether the stock needed for 130 servings is more or less than one-tenth of the tank's capacity.
1. Calculate the tank's capacity in litres and assess the supplier's claim of about 1,700 litres.
Read the worked answer
Volume of a cylinder: V = πr²h.
r = 0.6 m, h = 1.5 m. V = π × 0.6² × 1.5 = π × 0.36 × 1.5 = π × 0.54 ≈ 1.696 m³.
1 m³ = 1000 litres, so capacity ≈ 1,696 litres.
Using π ≈ 3.14 gives 0.54 × 3.14 = 1.6956 m³ ≈ 1,696 L. Using π ≈ 3.142 gives about 1,697 L.
The supplier's claim of "about 1,700 litres" is reasonable - it is within about 4 litres, well under 1% error. The claim should be accepted as an approximation, not as an exact figure.
2. Find the number of full 5-litre jugs the tank can supply, and compare the stock needed for 130 servings with one-tenth of the capacity.
Read the worked answer
Jugs: 1,696 ÷ 5 = 339.2, so 339 full jugs can be drawn (the remaining 0.2 of a jug, about 1 litre, is left over).
Stock scaling: 130 servings ÷ 40 servings = 3.25 batches. Stock needed = 3.5 × 3.25 = 11.375 litres.
One-tenth of capacity = 1,696 ÷ 10 ≈ 169.6 litres.
Comparison: 11.375 L is far less than 169.6 L - it is roughly 6.7% of one-tenth of the tank, or about 0.67% of the whole tank.
So the stock requirement is much less than one-tenth of the tank's capacity.