A school provides milk to its students in cylindrical glasses, each with a diameter of 7 cm. If each glass is filled with milk to a height of 12 cm, how many litres of milk are needed to serve 1600 students? Use 1000 cm3 = 1 litre.
Answer: One glass = 227 × 3.52 × 12 = 462 cm3; 1600 glasses = 7,39,200 cm3 = 739.2 litres.
Step-by-step solution
Given: Glass: diameter 7 cm (r = 3.5 cm), milk height 12 cm; 1600 students
To find: Milk needed in litres
To find: Milk needed in litres
Idea: Milk in one glass is a cylinder of radius 3.5 cm and height 12 cm. Multiply by 1600 and change cm3 to litres.
- Milk in one glass = πr2h = 227 × 3.5 × 3.5 × 12 = 38.5 × 12 = 462 cm3.1 mark
- For 1600 students: 1600 × 462 = 7,39,200 cm3.1 mark
- In litres: 7,39,200 ÷ 1000 = 739.2 litres.1 mark
739.2 litres of milk.
Check: Each student gets 0.462 L; 0.462 × 1600 = 739.2 L ✓.
Answer to write in the exam
Milk in one glass = 227 × 3.52 × 12 = 462 cm3
For 1600 glasses = 1600 × 462 = 7,39,200 cm3
∴ Milk needed = 739.2 litres
Common mistakes that cost marks
- Using 7 cm (the diameter) as the radius: the answer comes out four times too big.
- Dividing by 100 instead of 1000 to get litres.
How this can come in the exam
MCQ (1 mark)
A cylindrical glass of radius 3.5 cm is filled to 10 cm. It holds (π = 227)
- 385 mL
- 110 mL
- 770 mL
- 38.5 mL
Show answer
(A) 385 mL
38.5 × 10 = 385 cm3 = 385 mL.
Try one yourself
Juice is served in cylindrical cups of diameter 6 cm filled to 10 cm. How many litres serve 500 people? (π = 3.14)
Show answer
One cup = 3.14 × 9 × 10 = 282.6 cm3; 500 cups = 1,41,300 cm3 = 141.3 L.
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