![]() ![]() The formula for the surface area of a pyramid is: That's the option that we used as a pyramid in this surface area calculator. Regular means that it has a regular polygon base and is a right pyramid (apex directly above the centroid of its base), and square – means that it has this shape as a base. But depending on the shape of the base, it could also be a hexagonal pyramid or a rectangular pyramid one. When you hear a pyramid, it's usually assumed to be a regular square pyramid. A = π × r × √(r² + h²) + π × r² given r and h.Ī pyramid is a 3D solid with a polygonal base and triangular lateral faces.A = A(lateral) + A(base) = π × r × s + π × r² given r and s or.Finally, add the areas of the base and the lateral part to find the final formula for the surface area of a cone:.Thus, the lateral surface area formula looks as follows: R² + h²= s² so taking the square root we got s = √(r² + h²) But that's not a problem at all! We can easily transform the formula using Pythagorean theorem: Usually, we don't have the s value given but h, which is the cone's height.(sector area) = (π × s²) × (2 × π × r) / (2 × π × s)įor finding the missing term of this ratio, you can try out our ratio calculator, too! (sector area) / (large circle area) = (arc length) / (large circle circumference) so: ![]() The formula can be obtained from proportions, as the ratio of the areas of the shapes is the same as the ratio of the arc length to the circumference: The area of a sector - which is our lateral surface of a cone - is given by the formula:Ī(lateral) = (s × (arc length)) / 2 = (s × 2 × π × r) / 2 = π × r × s The arc length of the sector is equal to 2 × π × r. ![]() It's a circular sector, which is the part of a circle with radius s ( s is the cone's slant height).įor the circle with radius s, the circumference is equal to 2 × π × s. Let's have a look at this step-by-step derivation: The base is again the area of a circle A(base) = π × r², but the lateral surface area origins maybe not so obvious:
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