A net is the solid unfolded flat. Its total area is the surface area.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Count every face
A cuboid has six: three pairs of matching rectangles.
A cylinder
Two circles and one rectangle whose width is the circumference.
Units
Surface area is square units. Volume is cubic units. Mixing them is the commonest slip.
Unfold it and add the faces
Surface area is the total area of the net. For a prism that is two bases plus a rectangle whose width is the base perimeter. Thinking in terms of the net turns a three-dimensional problem into a two-dimensional one.
The cylinder's curved surface
Cut a cylinder's side and unroll it and you get a rectangle of height h and width 2πr, so the curved area is 2πrh. Adding two circles gives the total. The unrolling is worth doing once with paper.
The cone needs the slant height
A cone's curved surface area is πrl, where l is the slant height — found from the radius and vertical height by Pythagoras. This is the one place where slant height is the correct measurement to use.
Surface area and volume scale differently
Double every length and surface area quadruples while volume multiplies by eight. This is why large animals overheat less easily than small ones and why crushed ice melts faster than a block — the ratio changes with size.
Step 2: Try It Yourself
Tap and try it out.
- Cubes in one layer4 × 3 = 12
- Layers2
- 4 × 3 × 224 cubic units
Counting every cube gives 24, and so does 4 × 3 × 2. The formula is a shortcut for the count.
Step 3: Watch an Example
One step at a time.
Watch Kofi Unfold a Cuboid
A cuboid measures 4 by 3 by 2.
- Step 1
The two 4 by 3 faces give 12 each, so 24.
Step 4: Your Turn
Practice makes it stick.
The Cube
Problem 1 of 2
A cube with edge 3. What is its surface area?
The Faces
Problem 2 of 2
How many faces does a cuboid have?
Add the Faces
1 of 8
Cube with edge 2. Surface area?
2 of 8
Cube with edge 5. Surface area?
3 of 8
Cuboid 2 by 3 by 4. Surface area?
4 of 8
Cube with edge 2. Volume?
5 of 8
Are surface area units squared or cubed? 1 for squared, 2 for cubed.
6 of 8
How many faces does a triangular prism have?
7 of 8
A cylinder net has how many circles?
8 of 8
Sort each quantity by its units.
Tap something to move it.
- Empty
- Empty
- Empty
Step 5: Quick Check
Show what you know.
Question 1 of 1
Cube with edge 4. Surface area?
What You Learned
- A net is the solid unfolded, and its area is the surface area.
- Add every face — a cuboid has three matching pairs.
- Surface area is in square units; volume is in cubic units.