Try a sample first
Tap a sample chip to auto-fill dimensions and see the net right away.
Inputs & settings
Results
Share & copy
Copy the summary or LaTeX in one click.
Net (unfolded)
Face breakdown
| Face | Area |
|---|
Steps & validation
A sphere cannot be flattened without distortion; we show 4πr² as four circles of radius r.
How to use Surface & volume with nets effectively
What this calculator does
This calculator computes surface area and volume for common solids, then shows the corresponding net or geometric breakdown. It helps compare bases, lateral faces, sectors, slant height, and sphere formulas in one place.
Input meaning and unit policy
Choose the solid first, then enter the dimensions requested for that shape. Units are used consistently across every length input, and the output area and volume units follow from that choice.
Use-case sequence
Start with a sample chip, inspect the net, then replace one dimension at a time. Use the face breakdown to connect each area term with a visible face before copying the formula or result.
Common mistakes to avoid
Do not mix slant height and vertical height for pyramids or cones. For cylinders and cones, remember that the lateral face unfolds into a rectangle or sector, while a sphere cannot unfold into a perfect flat net without distortion.
Interpretation guidance
Use teacher mode when you need more formula steps for explanation. If the net and face table seem inconsistent, check the selected shape and unit before comparing the total surface area or volume.
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FAQ
What is the difference between surface area and lateral area?
Surface area sums every face; lateral area sums only the side faces. For prisms and cylinders, the p·h or 2πrh part is lateral, while the bases add 2B.
Why is a cylinder’s side a rectangle in the net?
Unfolding the side gives width 2πr (the circumference) and height h. The net makes this rectangle explicit.
Why does a cone net become a sector and how is the angle found?
The cone’s side opens into a sector with radius ℓ and arc 2πr. The central angle is α = 360·r/ℓ using ℓ = √(r²+h²).
Can a sphere be unfolded?
No. A perfect sphere cannot form a flat net without stretching. We show the 4πr² idea as four circles; craft gores are approximate.
How should I check a net diagram?
Start by matching each face in the net to the shape: bases, lateral faces, and any sector or rectangle formed by unfolding. Then compare the face breakdown table with the formula steps.
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