GCSE · Geometry and measures
Cylinder and cone nets
Unwrap a cylinder or cone and connect the curved surface to a rectangle or sector.
Switch between cylinder and cone. Change the radius and compare the matching boundary lengths.
Scroll the diagram sideways to see every label.
The rectangle wraps around once; its length is 18.85 cm.
- Base circumference
- 6π ≈ 18.85 cm
- Curved area
- 75.398 cm²
- Total area
- 131.947 cm²
- Volume
- 113.097 cm³
The two discs are shown tangent to the rectangle for display. Their curved boundaries meet the two straight edges when assembled; those edges each have length 2πr.
Predict, test and explain
Step 1 of 3
Predict
Which length wraps around a cylinder’s base?
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.
Which length wraps around a cylinder’s base?
Hint
The complete base circumference must meet the curved surface with no gap or overlap.
Reveal answer
The complete base circumference must meet the curved surface with no gap or overlap.
Build an explanation
Hint 1
The complete base circumference must meet the curved surface with no gap or overlap.
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.
A cone has radius 3 cm and perpendicular height 4 cm. Find its curved and total surface areas.
- Use Pythagoras to find slant height √(3² + 4²) = 5 cm.
- Curved area = πrl = 15π cm².
- Add the circular base: 15π + 9π.
Answer: Curved 15π cm²; total 24π cm².
Connect this idea
Watch out: The complete base circumference must meet the curved surface with no gap or overlap.