Cone Surface Area Calculator

SA = πr² + πrl, where l = √(r² + h²) is the slant height.

Inputs

Result

Surface area (with base)
174.0299
Lateral 123.76 + base 50.27.
  • Radius4
  • Height9
  • Slant height9.848858
  • Lateral surfaceπr × slant123.764397
  • Base circleπr²50.265482
  • Total SA (closed)174.029880
  • Open SA (no base)123.764397
  • Volume150.796447

Step-by-step

  1. Slant height = √(r² + h²) = √(4² + 9²) = 9.8489.
  2. Lateral surface = πr × slant = 123.7644.
  3. Base = πr² = 50.2655.
  4. Total = 174.0299.

How to use this calculator

  • Enter base radius and height.
  • Read SA (with or without base).

About this calculator

A cone's surface has two parts: lateral (curved side) and base (circle). Lateral surface = πr × slant, where slant = √(r² + h²). Total SA = πr² + πr × slant = πr(r + slant). Many real cones are open (party hats, ice cream cones) — use just the lateral. The lateral, when unrolled, is a circular sector of radius = slant, arc-length = circumference of base = 2πr.

Frequently asked

The lateral surface, when flattened, is a circle sector with radius = slant and arc length = 2πr (the cone's base circumference).

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