Respuesta :
Answer:
[tex]\pi r \sqrt{r^2+h^2}[/tex]
Step-by-step explanation:
Given that there is a cone with radius r and slant height s.
We know that lateral surface area of the cone is
=[tex]\pi r s[/tex]
Alternately if instead of s, h is known we can write this in terms of h also.
Consider the right triangle formed by slant height, height and radius of the cone.
Using Pythagorean theorem we have
[tex]s^2=r^2+h^2[/tex]
Or [tex]s=\sqrt{r^2+h^2}[/tex]
Hence lateral surface area of the cone
=[tex]\pi r \sqrt{r^2+h^2}[/tex]
