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Volume and Capacity Formulas

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Volume and Capacity Formulas

Help plan a recycling drive. Calculate volumes and capacities, show your working, and include units. Use π ≈ 3.14 where needed. Remember: 1 cm³ = 1 mL and 1,000 cm³ = 1 L.

Formula toolkit

Use these formulas: cube V = s³; rectangular prism V = l × w × h; cylinder V = πr²h. Capacity describes how much a container can hold.

1.Match each symbol with what it represents in the formulas: s, l, w, h, r. Meanings: side length, length, width, height, radius.

Length
Radius
Height
Side length
Width

2.The collection crate is a cube with sides of 0.4 m. Calculate its volume in m³ and in litres.

3.A rectangular collection box measures 60 cm long, 35 cm wide and 40 cm high. Find the box’s volume in cm³, then express it in litres.

4.A cylindrical bottle has radius 4 cm and height 20 cm. Calculate its volume to the nearest cubic centimetre.

5.A collected drink-container rinse-water volume is 2.6 L. How many cubic centimetres is this? Show the conversion.

6.The team has a 1.5 L measuring jug. How many millilitres can it hold?

Choose the right container

Compare the containers before deciding what to use.

7.A rectangular carton is 15 cm long, 10 cm wide and 24 cm high. Which expression gives its volume?

15 + 10 + 24
15 × 10 × 24
3.14 × 15² × 24
15 × 10

8.Container A is a cube with side length 20 cm. Container B is a cylinder with radius 10 cm and height 20 cm. Which has the greater volume, and by how much?

9.A cylindrical bin has radius 0.5 m and height 1.2 m. Calculate its volume in m³, then convert its capacity to litres.

10.A rectangular container has a volume of 12,000 cm³. Its base is 30 cm by 20 cm. Find its height.

11.Select every correct statement about volume and capacity.

Volume measures the space occupied by a three-dimensional object.
Capacity is the amount a container can hold.
1 cm³ is equal to 1 mL.
1 m³ is equal to 100 L.

12.The team wants to fit exactly 24 L of sorted material into identical rectangular tubs. Each tub measures 40 cm × 25 cm × 20 cm. How many tubs are needed to hold all the material? Show why.