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Surface & volume with nets

Learn surface area and volume for prisms, pyramids, cylinders, cones, and spheres with synced 3D sketches and unfoldable nets. See lateral/base breakdowns, slant height, units, and step-by-step formulas.

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Try a sample first

Tap a sample chip to auto-fill dimensions and see the net right away.

How to use (3 steps)

    Inputs & settings

    Results update automatically as you type. π mode applies to cylinders, cones, and spheres.

    Results

    Share & copy

    Copy the summary or LaTeX in one click.

    Net (unfolded)

    Base Lateral Cylinder net: width 2πr, height h.

    Face breakdown

    FaceArea

    Steps & validation

    A sphere cannot be flattened without distortion; we show 4πr² as four circles of radius r.

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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.

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