SOLUTION: Prove that the surface area of a cone without its base circle is A=pirs, where r is the base radius and s is the slant height of the cone. I have even been provided with solutio

Algebra ->  Surface-area -> SOLUTION: Prove that the surface area of a cone without its base circle is A=pirs, where r is the base radius and s is the slant height of the cone. I have even been provided with solutio      Log On


   

Question 1142527: Prove that the surface area of a cone without its base circle is A=pirs, where r is the base radius and s is the slant height of the cone.
I have even been provided with solutions but I don't understand them! If you would like to see the answers, just reply back saying so. Thank you!
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The basic formula for the lateral surface area of a cone is


    A = %281%2F2%29%2AH%2As,      (1)


where A is the lateral surface area, H is the slant height and "s" is the circumference of the base of the cone.


When students study the lateral surface area of a cone, they start from this formula, so I will assume that you are familiar with it.



    If not, then you can derive it mentally and momentarily in your mind, presenting the lateral surface area 

    of  cone as the union of surface area of many narrow triangles with the common peak vertex at the cone's vertex.



The last step in my explanation is the formula  


    s = 2%2Api%2Ar      (2)


for the base circumference.  Here  "r"  is the cone's radius (= the radius of the base).


As soon as you substitute  (2)  into (1), you will obtain what you need.


Explained and answered.