Problem-solving & missing dimensions
Once you know that volume = length × width × height, you can solve real problems — and you can also work backwards: if you know the volume and two of the dimensions, you can find the third.
Apply the formula
Q1. A fish tank is 40 cm long, 25 cm wide and 30 cm high. What is its volume in cubic centimetres?
Q2. A shipping carton measures 8 by 5 by 3 units. A second carton is twice as tall but the same length and width. Find the volume of each carton.
Find the missing dimension
Q3. Use the box in the picture. Its volume is 48 cubic centimetres, its length is 6 cm and its width is 4 cm. Work backwards to find the height. Hint: how many cubes are in one layer?
Q4. A prism has a volume of 60 cubic units. Its base is 5 long and 3 wide. How tall is it?
Q5. A box holds 36 centimetre cubes. It is 3 cm high. List two possible length-and-width pairs for its base.
Q6. Reasoning. To find a missing height, Maya divided the volume by the area of the base. Explain why dividing works, using the idea of layers.
Answer key (teacher use)
Suggested answers for the questions in this worksheet.
Q1. 40 × 25 × 30 = 30 000 cubic centimetres.
Q2. First carton: 8 × 5 × 3 = 120 cubic units. Second carton (twice as tall): 8 × 5 × 6 = 240 cubic units.
Q3. One layer = 6 × 4 = 24 cubes. Number of layers = 48 ÷ 24 = 2. Height = 2 cm.
Q4. Base = 5 × 3 = 15. Height = 60 ÷ 15 = 4. Height = 4 units.
Q5. One layer must hold 36 ÷ 3 = 12 cubes. Any two length–width pairs that multiply to 12: e.g. 6 × 2, 4 × 3, 12 × 1.
Q6. The base area is the number of cubes in one layer. The height is how many of those layers stack up, so dividing the total volume by the area of the base tells you how many layers there are — that is the height. (Volume = base × height, so height = volume ÷ base.)