Volume of everyday objects · 5 marks

Activity: Find the approximate volumes of a gas cylinder, a bucket, any cylindrical vessel, a cupboard, a water tank that you can find near you (use 1000 cm³ = 1 litre).

Answer: With sample measurements (π = 3.14): gas cylinder ≈ 35 L, bucket ≈ 17 L, cooking vessel ≈ 5.7 L, cupboard ≈ 810 L, cylindrical water tank ≈ 1190 L. Your own numbers will differ with your measurements.

Step-by-step solution

Idea: Model each object as the nearest simple solid (cylinder or cuboid), measure the inside, find the volume in cm³ and divide by 1000 to get litres.

Gas cylinder (model: cylinder). Inside diameter ≈ 30 cm (r = 15 cm), body height ≈ 50 cm. V = πr²h = 3.14 × 225 × 50 = 35 325 cm³ ≈ 35 L.1 mark
Bucket (wider at the top, so use the average diameter). Top 30 cm, bottom 24 cm, average 27 cm (r = 13.5 cm), height 30 cm. V ≈ 3.14 × 182.25 × 30 ≈ 17 168 cm³ ≈ 17 L.1 mark
Cylindrical vessel (cooking pot). Diameter 22 cm (r = 11 cm), height 15 cm. V = 3.14 × 121 × 15 ≈ 5699 cm³ ≈ 5.7 L.1 mark
Cupboard (model: cuboid). 90 cm × 50 cm × 180 cm = 8,10,000 cm³ = 810 L.1 mark
Water tank (cylindrical plastic tank). Diameter 110 cm (r = 55 cm), height 125 cm. V = 3.14 × 3025 × 125 ≈ 11,87,313 cm³ ≈ 1190 L (sold as a ‘1000-litre’ tank, as it is never filled to the very top).1 mark

Sample results: gas cylinder ≈ 35 L, bucket ≈ 17 L, vessel ≈ 5.7 L, cupboard ≈ 810 L, water tank ≈ 1190 L (π = 3.14; 1000 cm³ = 1 L).

Check: Compare with labels: a domestic LPG cylinder holds about 33 L of water, buckets are sold as 15–20 L, and roof tanks as 1000 L, so the estimates are sensible ✓.

Answer to write in the exam

Gas cylinder: V = 3.14 × 15² × 50 = 35 325 cm³ ≈ 35 L

Bucket: V ≈ 3.14 × 13.5² × 30 ≈ 17 168 cm³ ≈ 17 L

Vessel: V = 3.14 × 11² × 15 ≈ 5699 cm³ ≈ 5.7 L

Cupboard: V = 90 × 50 × 180 = 8,10,000 cm³ = 810 L

Water tank: V = 3.14 × 55² × 125 ≈ 11,87,313 cm³ ≈ 1190 L

Common mistakes that cost marks

Measuring the outside instead of the inside of a container; the walls take up space.
Dividing cm³ by 100 instead of 1000 to get litres.
Using the diameter as the radius, which makes cylinder volumes four times too big.

How this can come in the exam

Case-based (4 marks)

Riya measures her family’s cylindrical water drum: inside diameter 56 cm, height 80 cm. They use about 150 L of water a day from it.
(i) Find the drum’s volume in cm³. (ii) Convert it to litres. (iii) For how many full days does a full drum last? (iv) If the drum is only filled to 75 cm, how many litres does it hold? (π = 227)

Show answer

(i) 227 × 28² × 80 = 1,97,120 cm³ (1 mark). (ii) 197.12 L (1 mark). (iii) 197.12 ÷ 150 ≈ 1.3, so 1 full day (1 mark). (iv) 227 × 784 × 75 = 1,84,800 cm³ = 184.8 L (1 mark).

Try one yourself

A cuboidal fridge compartment is 50 cm × 40 cm × 60 cm inside. What is its capacity in litres?