What are Volume Word Problems?
Understanding volume is an important part of GCSE maths. Many real-world problems involve calculating how much space a solid occupies, or how much material is needed to cover it. To solve these problems, you’ll need to:
- Convert units carefully (e.g. m to cm, cm to mm).
- Recall key formulas for volume and surface area.
- Apply reasoning to practical contexts such as containers, pools, or packaging.
Worked Example
Let’s start with an example:
Question
A cuboid has length 3m, width 50cm, and height 200mm. Find its volume in cubic centimetres.
Step 1: Convert all units to cm
Step 2: Apply the cuboid volume formula
Practice Questions and Solutions
A prism has a base area of 12dm² and a capacity of 48 litres. Find its height.
Convert:
Using:
Therefore:
The height of a cylinder equals the circumference of its base. Height = 125.66cm. Find surface area and volume.
Using:
A cathedral dome is a hemisphere with radius 50m. Restoration costs £300 per m², how much will it cost to restore the entire dome?
Using:
A cylindrical container (radius 10cm, height 5cm) is filled with water. Mass of filled container = 2kg. Find the mass of the empty container.
Using:
Given the density of water:
Mass of water = 1.57kg
Mass of container = 2 - 1.57 = 0.43kg
Louis makes 10 conical hats (radius 15cm, slant height 25cm). How much cardboard is used?
Using:
For 10 hats:
A cube with edge 20cm is filled with water. Would it fit inside a sphere with radius 20cm?
Calculate cube volume:
Calculate sphere volume:
Given the volume of the sphere is more than 4 times that of the cube, we can conclude that the water will easily fit.
How many square tiles (20cm × 20cm) are needed to cover the sides and base of a pool 10m × 6m × 3m?
Area of base =
Area of two long sides =
Area of two short side =
Area of each tile:
No. of tiles required =
Four ice cubes of side 4cm melt in a cylindrical glass of radius 6cm. How high will the water rise?
Total volume of ice =
Volume of water in glass = base area × height
Therefore base area =
A moving company is trying to store boxes in a storage room with length 5m, width 3m and height 2m. How many boxes can fit in this space if each is 10cm long, 6cm wide and 4cm high?
Room volume =
Box volume =
Number of boxes =
A swimming pool is 8m long, 6m wide and 1.5m deep. The water-resistant paint needed for the pool costs £6 per m².
- How much will it cost to paint the interior surfaces of the pool?
- How many litres of water will be needed to fill it?
Surface area of base =
Surface area of long sides =
Surface area of short sides =
Total area =
Water Volume =
Did you like this article? Rate it!
Loading...
What is frac and sqrt
Interested learning more