Volume of Cubes and Cuboids

Area covers a flat shape; volume fills a solid one — it is the amount of space inside a box, a tank, or a water bottle. Because a cuboid is just a stack of identical layers, its volume formula is wonderfully simple. Get it right and you can solve every fish-tank and water-pouring problem the PSLE throws at you.

Parents: ask your child to predict whether a question wants area or volume before they reveal. The "Method tip" boxes name the exact formula and unit a PSLE marker rewards.

By the end you'll be able to find the volume of cubes and cuboids, the volume of liquid, use base area times height, and find an unknown edge. Let's fill it up.

Volume of a cube and a cuboid

Volume is the space inside a solid. A cuboid has volume length × width × height. A cube has all edges equal, so its volume is edge × edge × edge.

For example, a cuboid 5 cm by 4 cm by 3 cm has volume 5 × 4 × 3 = 60 cubic cm. A cube of edge 2 cm has volume 2 × 2 × 2 = 8 cubic cm. Because you multiply three lengths, the unit is always cubic cm or cubic m.

Base area times height

There is a neat way to see the formula. The bottom of a cuboid is a rectangle with a base area of length × width. Volume is just that base area × height — like stacking that rectangle upwards.

For example, if the base area is 12 square cm and the height is 5 cm, the volume is 12 × 5 = 60 cubic cm. This view is handy when a question gives you the base area directly instead of the two base lengths.

Volume of liquid

When a cuboid tank holds water, the water itself forms a cuboid. Its volume is length × width × water height — using the height the water reaches, not the full height of the tank.

A useful link to remember: 1 litre = 1000 cubic cm. So a volume in cubic cm can be changed to litres by dividing by 1000. For example, water 10 cm by 10 cm by 5 cm deep has volume 10 × 10 × 5 = 500 cubic cm, which is 0.5 litre.

Finding an unknown edge

You can also work backwards. If you know the volume and two of the lengths, divide to find the missing edge. This is just the volume formula rearranged.

For example, a cuboid has volume 60 cubic cm, length 5 cm and width 4 cm. The base area is 5 × 4 = 20, so the height is 60 ÷ 20 = 3 cm. Find the base area first, then divide the volume by it.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is the volume of a cube with edge 4 cm?

   12 cubic cm16 cubic cm64 cubic cm

2. What is the volume of a cuboid 8 cm by 5 cm by 2 cm?

   15 cubic cm80 cubic cm40 cubic cm

3. A cuboid has a base area of 15 square cm and a height of 6 cm. What is its volume?

   21 cubic cm90 cubic cm45 cubic cm

4. A tank base is 10 cm by 10 cm. Water fills it to a height of 8 cm. What is the volume of water?

   800 cubic cm80 cubic cm180 cubic cm

5. A cuboid has a volume of 48 cubic cm, a length of 4 cm and a width of 2 cm. What is its height?

   6 cm8 cm12 cm

6. A container holds 2000 cubic cm of water. How many litres is that?

   2 litres20 litres0.2 litres

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