Surface Area and Volume • Topic 2 of 7

Cuboids

A cuboid (rectangular box) has length, width and height, which may all differ. Its volume is length × width × height — the number of unit cubes that fill it. For a box 4 by 3 by 2, the volume is 24. Volume is in cubic units. The three dimensions can be multiplied in any order. If you know the volume and two dimensions, divide to find the third. Cuboid volume is one of the most common SAT solid-geometry tasks, appearing in tank, box and container problems. Keep it separate from surface area, which adds the areas of all six rectangular faces.

An oblique rectangular box with length, width and heightCuboid (rectangular box)lhwVolume = l × w × h

✅ Solved examples

1. A box is 4 by 3 by 2. Find its volume.
4 × 3 × 2 = 24.
2. A box is 5 by 5 by 2. Find its volume.
5 × 5 × 2 = 50.
3. A box is 6 by 4 by 3. Find its volume.
6 × 4 × 3 = 72.
4. A box has volume 60 with base 5 by 4. Find its height.
60 ÷ 20 = 3.

✏️ Practice — try these, take hints as needed

1. A box is 3 by 3 by 3. Find its volume.
l × w × h.
3 × 3 × 3.
—
27.
2. A box is 6 by 2 by 2. Find its volume.
6 × 2 × 2.
—
—
24.
3. A box is 8 by 5 by 2. Find its volume.
8 × 5 × 2.
—
—
80.
4. A box is 7 by 3 by 4. Find its volume.
7 × 3 × 4.
—
—
84.
5. A box has volume 48 with base 4 by 3. Find its height.
48 ÷ 12.
—
—
4.

📝 Topic test — 8 questions

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