The same cylinder gives you two different measurements. Volume tells you how much space is inside. Surface area tells you how much area its outside covers. A jar label only covers the curved wall, while wrapping the entire jar also covers both circular ends.
Use a cylinder 4 cm across and 5 cm tall. These dimensions let you check the numbers by hand and see how changing the radius affects each result.
Measure across the center and halve the diameter
The visualizer asks for the radius, which runs from the center of the circular end to its edge. A diameter of 4 cm gives a radius of 2 cm. The height is the perpendicular distance between the two ends.
The browser tool shows numbers without unit labels. Enter both dimensions in the same unit. With centimeter inputs, the volume is in cubic centimeters and the area is in square centimeters.
Check the volume and the area of a closed cylinder
The area of the circular base is π × 2² = 4π cm². Multiplying that by the height gives a volume of 20π cm³. For the outside area, add the curved wall (20π cm²) and both ends (4π cm² each) to get 28π cm².
- Open the 3D Shape Visualizer, select Cylinder, and set Radius to 2 and Height to 5.
- In Properties, check Volume, Surface Area, and Diameter against the results below.
- Switch to Top to see the circular end, then to Front to see the height. The dimensions and results stay the same as you change the view.
Input
Shape: Cylinder
Radius: 2
Height: 5Expected result
Volume: 62.83 cm³
Surface area: 87.96 cm²
Diameter: 4.00 cmUse the curved wall area for a wraparound label
Imagine cutting the curved wall along its height and flattening it. The resulting rectangle is 5 cm high and one circumference wide, which is 4π cm or about 12.57 cm. Its area is 20π cm², about 62.83 cm². Add any overlap or trim allowance separately.
For a cylinder with one open end, count the curved wall and one circular base. That gives 24π cm², about 75.40 cm². Use the internal dimensions when estimating the capacity of a container with thick walls. Keep π in the calculation and round the final result.
Double the dimensions and compare the results
Set Radius to 4 and Height to 10. The closed surface area rises to 351.86 cm², four times the original area before rounding. The volume rises to 502.65 cm³, eight times the original volume before rounding. Area multiplies two lengths, while volume multiplies three.
Restore the original settings, then change only the height from 5 to 10. The volume doubles to 125.66 cm³ and the curved wall area doubles, while the area of each end stays fixed. This is why the total surface area rises to 150.80 cm².
Try the tools
Start with the worked example above, then try the tool with your own inputs.
References and corrections
Found a result that differs from this guide? Send a correction with a small, non-sensitive example and your expected result.