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Cone Total Surface Area

Also known as surface area of a cone · cone area with base

A=πr(r+l)A = \pi r (r + l)

Worked example: Cone r = 3 m, l = 5 m → 24 pi m2 (15 pi side + 9 pi base) — press Try an example to run it live, then adjust anything.

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Constant used — built into this formula, no need to enter
π=3.141592653589793\pi = 3.141592653589793Pi · exact
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Cone Total Surface Area explained

rlA

Add the base disc to the curved side and you get the whole skin of a solid cone: πrl+πr2\pi r l + \pi r^2, which factors neatly to A=πr(r+l)A = \pi r(r + l). The factored form is the one worth remembering, because it makes the structure obvious: one πr\pi r multiplying a length that is part radius, part slant.

Whether you actually want the base is a judgement call the formula cannot make for you. Painting a conical spire? The base is the open bottom, so use the lateral area alone. Anodising a machined cone, sizing shrink-wrap for a pile of sand, or costing the sheet for a closed conical tank end? Then the base counts and this is your number.

Solving backwards for the radius is a quadratic, since rr appears squared in the base term. Both roots exist algebraically but only the positive one is a cone, which is why the solver returns r=12(−l+l2+4A/π)r = \tfrac{1}{2}\left(-l + \sqrt{l^2 + 4A/\pi}\right) and nothing else.

Cone Total Surface Area formula

A=πr(r+l)A = \pi r (r + l)
Where
  • AA= Total surface area (m²)
  • rr= Base radius (m)
  • ll= Slant height (m)

Missing one of these? Work it out first, then come back