Lateral Surface Area of Right Circular Cone

Theorem

Let $K$ be a right circular cone.

Let $r$ be the radius of the base of $K$.

Let $s$ be the slant height of $K$.

Then the area $\AA$ of the lateral surface of $K$ is given by:

$\AA = \pi r s$

Proof

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Also presented as

The can also be expressed in the form:

$\AA = \pi r \sqrt {r^2 + h^2}$

where:

$r$ is the radius of the base

$h$ is the height.

Sources

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Right Circular Cone of Radius $r$ and Height $h$: $4.38$
1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cone
2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cone
2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Right Circular Cone of Radius $r$ and Height $h$: $7.38.$
2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): cone
2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $1$: Areas and volumes
2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): cone
2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $1$: Areas and volumes