GCSE · Geometry and measures
Surface area: every face counts
Highlight each face of a cuboid and compare a closed box with an open tray.
Compare Closed box and Open tray using the same dimensions. Find exactly which area is removed.
Scroll the diagram sideways to see every label.
| Face | Area |
|---|---|
| Base | 24 cm² |
| Front | 18 cm² |
| Back | 18 cm² |
| Left | 12 cm² |
| Right | 12 cm² |
| Lid | 24 cm² |
Six faces: three equal pairs.
- Surface area
- 108 cm²
- Volume / capacity
- 72 cm³
- Highlighted area
- 108 cm²
Drawings ignore wall thickness. Highlighted faces can be on the far side; use the rotation control to bring them into view.
Predict, test and explain
Step 1 of 3
Predict
Does removing the lid change a box’s capacity?
Explore and compare
Choose the investigation above. Predict what will change before you move a control.
Try it in the simulation. Change one thing at a time.
Notes and saved values stay in this tab. They disappear when you reload.
Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
Does removing the lid change a box’s capacity?
Hint
Surface area uses square units; capacity is a volume measured in cubic units.
Reveal answer
Surface area uses square units; capacity is a volume measured in cubic units.
Build an explanation
Hint 1
Surface area uses square units; capacity is a volume measured in cubic units.
Hint 2
Use the labels and units in the live model to check your method.
Hint 3
Explain which lengths, areas or volumes are being compared.
Worked example
This example uses fixed values, separate from the diagram controls.
An open tray is 6 cm by 4 cm by 2 cm. Find its surface area, ignoring thickness.
- Base area = 6 × 4 = 24 cm².
- Two long walls contribute 2 × 6 × 2 = 24 cm².
- Two short walls contribute 2 × 4 × 2 = 16 cm².
Answer: 64 cm².
Connect this idea
Watch out: Surface area uses square units; capacity is a volume measured in cubic units.