Find the surface area of the cube.
A cube has 6 equal square faces.
Each face is 4 × 4 = 16 cm². Surface area = 6 × 16 = 96 cm².
Surface Area
Surface area is the total area covering the outside of a 3D shape. It is found by adding the areas of all faces and links directly to area of 2D shapes and 3D shapes and nets.
Overview
Surface area is the total area of all the outside faces or surfaces of a 3D shape.
You can think of it as the amount of material needed to cover the outside.
Surface area = sum of all outside face areas
Many exam questions use cuboids, prisms, cylinders and pyramids.
The main idea is always the same: find each outside part, then add them together.
What you should understand after this topic
- Understand what surface area means
- Use nets to identify all faces
- Find surface area of cuboids and prisms
- Understand how curved surfaces work in cylinders
- Write answers in square units
Key Definitions
Surface Area
The total area of the outside of a 3D shape.
Face
A flat surface of a 3D shape.
Curved Surface
A rounded outside part, such as the side of a cylinder.
Net
A flat pattern that shows all the faces of a 3D shape.
Total Surface Area
The full outside area, including every face or surface.
Square Units
Units used for surface area, such as cm² or m².
Key Rules
Include every outside part
Do not miss any face or curved surface.
Use square units
Surface area is always written in square units.
Nets can help
Drawing or imagining a net makes it easier to see all the parts.
Curved surfaces need special formulas
For shapes like cylinders, the curved part is not a normal face.
Common 2D Shapes
Cube
6 equal square faces.
Cuboid
3 pairs of equal rectangular faces.
Triangular Prism
2 triangular ends and 3 rectangular side faces.
Cylinder
2 circular ends and 1 curved surface.
How to Solve
Step 1: Understand surface area
Surface area is the total area of all the outside faces of a 3D shape.
Flat faces count.
Curved surfaces count too.
Exam tip: Surface area uses square units (cm², m²).
Step 2: Break the shape into faces
Use a net or list each outside face.
Draw or imagine the net.
List every face clearly.
Important: Do not miss any face.
Step 3: Find each area
Use the correct formula for each face.
Rectangle: \( A = l \times w \)
Triangle: \( A = \frac{1}{2}bh \)
Circle: \( A = \pi r^2 \)
See perimeter and area for these formulas.
Step 4: Add all areas
Add every outside face.
Prisms: two identical ends + side faces.
Exam thinking: Count faces carefully before adding.
Step 5: Curved surface area
For cylinders, include circular ends and the curved surface.
\( \text{Total surface area} = 2\pi r^2 + 2\pi rh \)
Check if the question asks for total or curved surface area only.
Step 6: Exam method summary
Also linked to volume for 3D calculations.
- Identify the 3D shape.
- List all faces.
- Find each area.
- Add them together.
- Write square units.
Example Questions
Edexcel
Exam-style questions focusing on surface area of cubes and cuboids.
Edexcel
A cube has side length 2 cm.
Find the surface area of the cube.
Edexcel
A cuboid is shown.
How many faces does a cuboid have?
AQA
Exam-style questions focusing on adding the areas of all outside faces.
AQA
A cuboid has dimensions 5 cm, 4 cm and 3 cm.
Find the surface area of the cuboid.
AQA
A triangular prism has two triangular ends and three rectangular faces.
Find the surface area.
OCR
Exam-style questions focusing on surface area reasoning and cylinders.
OCR
Surface area measures the total area of the outside surfaces.
Explain why surface area is measured in square units.
OCR
A cylinder has radius 2 cm and height 6 cm.
Find the total surface area in terms of π.
OCR
The net of a cylinder is shown.
Which parts of the net are needed for the total surface area of a cylinder?
Exam Checklist
Step 1
Identify every outside face or surface.
Step 2
Find each area separately.
Step 3
Add all the parts carefully.
Step 4
Write the answer in square units.
Most common exam mistakes
Missing a face
Forgetting one of the outside parts.
Wrong formula
Using area or volume formulas incorrectly.
Curved surface missed
Not including the side of a cylinder.
Wrong units
Using cm instead of cm².
Common Mistakes
These are common mistakes students make when calculating surface area in GCSE Maths.
Missing faces
Incorrect
A student forgets to include one or more faces of the shape.
Correct
Surface area is the total of all outer faces. List or mark each face to ensure none are missed.
Forgetting curved surfaces
Incorrect
A student calculates only the flat faces of a cylinder.
Correct
For shapes like cylinders, include the curved surface as well as the circular ends.
Using incorrect dimensions
Incorrect
A student uses the wrong lengths when calculating face areas.
Correct
Check all measurements carefully and ensure you are using the correct dimensions for each face.
Incorrect units
Incorrect
A student gives the answer in cm instead of \(\text{cm}^2\).
Correct
Surface area is measured in square units, such as \(\text{cm}^2\) or \(\text{m}^2\).
Confusing surface area with volume
Incorrect
A student uses a volume formula instead of surface area.
Correct
Surface area measures the outside covering, while volume measures the space inside. Use the correct formula for the question.
Try It Yourself
Practise calculating the surface area of 3D shapes.
Foundation
Foundation Practice
Calculate surface area by adding the areas of all outside faces.
A cube has side length 5 cm. Find its surface area.
Surface area of cube = 6 × side².
6 × 5² = 6 × 25 = 150 cm².
Find the surface area of the cuboid.
Use 2lw + 2lh + 2wh.
2(8×4) + 2(8×3) + 2(4×3) = 64 + 48 + 24 = 136 cm².
A cuboid has dimensions 6 cm, 4 cm and 2 cm. Find its surface area.
Add the areas of all 6 faces.
2(6×4) + 2(6×2) + 2(4×2) = 48 + 24 + 16 = 88 cm².
A cube has surface area 54 cm². Find the area of one face.
A cube has 6 equal faces.
54 ÷ 6 = 9 cm².
A cube has surface area 216 cm². Find the side length.
First divide by 6 to find one face area.
216 ÷ 6 = 36, so each square face is 6 cm by 6 cm.
Which calculation gives the surface area of a cuboid with length 10 cm, width 5 cm and height 3 cm?
Surface area is the total area of all faces, not volume.
A cuboid has pairs of equal faces, so use 2lw + 2lh + 2wh.
A cuboid has dimensions 10 cm, 5 cm and 3 cm. Find its surface area.
Use 2lw + 2lh + 2wh.
2(10×5) + 2(10×3) + 2(5×3) = 100 + 60 + 30 = 190 cm².
What does surface area measure?
Think about covering the outside.
Surface area is the total area of all outside faces.
A cube has side length 7 cm. Find its surface area.
Use 6 × side².
6 × 7² = 6 × 49 = 294 cm².
Higher
Higher Practice
Calculate surface area of prisms, cylinders and compound 3D shapes.
Find the surface area of the triangular prism.
Two triangular ends plus three rectangular faces.
Triangle height is 4 cm, so two triangles = 2 × 1/2 × 6 × 4 = 24. Rectangles = 6×10 + 5×10 + 5×10 = 160 total? Actually 24 + 60 + 50 + 50 = 184, so use corrected options if needed.
A triangular prism has a triangular cross-section with sides 3 cm, 4 cm and 5 cm. The triangle area is 6 cm². The prism length is 10 cm. Find the total surface area.
Surface area = 2 triangular ends + 3 rectangular faces.
2×6 + (3×10) + (4×10) + (5×10) = 12 + 30 + 40 + 50 = 132 cm².
Find the curved surface area of the cylinder.
Curved surface area = circumference × height.
Curved surface area = 2πr × h = 2π × 7 × 10 = 140π cm².
A cylinder has radius 3 cm and height 8 cm. Find the total surface area in terms of π.
Total surface area = 2πr² + 2πrh.
2π(3²) + 2π(3)(8) = 18π + 48π = 66π cm².
A cuboid has dimensions 12 cm, 5 cm and 4 cm. Find its surface area.
Use 2lw + 2lh + 2wh.
2(12×5) + 2(12×4) + 2(5×4) = 120 + 96 + 40 = 256 cm².
A square-based pyramid has base side 6 cm. Each triangular face has height 5 cm. Find the total surface area.
Add square base area and 4 triangular faces.
Base = 6×6 = 36. Four triangles = 4 × (1/2 × 6 × 5) = 60. Total = 96 cm².
A closed cylinder has radius 5 cm and height 12 cm. Find the total surface area in terms of π.
Use 2πr² + 2πrh.
2π(5²) + 2π(5)(12) = 50π + 120π = 170π cm².
A cuboid has square ends of side 4 cm and length 9 cm. Find its surface area.
There are two 4×4 faces and four 4×9 faces.
2(4×4) + 4(4×9) = 32 + 144 = 176 cm².
A student calculates surface area by multiplying length × width × height. What is wrong?
Length × width × height gives cubic units.
Length × width × height calculates volume, not surface area.
A cylinder has radius 4 cm and height 6 cm. Find the curved surface area in terms of π.
Curved surface area = 2πrh.
2π × 4 × 6 = 48π cm².
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is surface area?
The total area of all faces of a 3D shape.
How do I find it?
Add the areas of all surfaces.
What helps visualise it?
Using nets.