SOLUTION: fIND THE SURFACE AREA OF A RIGHT CONE WITH A A BASE RADIUS OF 6 CM AND HEIGHT OF 6 TIMES THE SQUARE ROOT OF 3 CM?

Algebra ->  Surface-area -> SOLUTION: fIND THE SURFACE AREA OF A RIGHT CONE WITH A A BASE RADIUS OF 6 CM AND HEIGHT OF 6 TIMES THE SQUARE ROOT OF 3 CM?      Log On


   

Question 173197: fIND THE SURFACE AREA OF A RIGHT CONE WITH A A BASE RADIUS OF 6 CM AND HEIGHT OF 6 TIMES THE SQUARE ROOT OF 3 CM?
Answer by colliefan(242) About Me  (Show Source):
You can put this solution on YOUR website!
Area of the base is pi+%2A+r%5E2
Area of the cone is pi * r * s, where r is the radius and s the distance from the apex of the cone to the base.
The area of the whole figure then is A = pi+%2A+r%5E2++%2B+pi+%2A+r+%2A+s

You are given the value of r, but not of s. You can calculate though because it is the hypotenuse of a right triangle with s and h as its legs. From the Pythagorean theorem, a%5E2+%2B+b%5E2+=+c%5E2

6%5E2+%2B+%286sqrt%283%29%29%5E2+=+s%5E2
36+%2B+36%2A3+=+s%5E2
144+=+s%5E2
s = 12

Substitute the values of s and r in the above equation to calculate the area
A = pi+%2A+r%5E2++%2B+pi+%2A+r+%2A+s
If you factor the Pi from both terms:
A = Pi+%2A+%28r%5E2+%2B+rs%29
A = Pi+%286%5E2+%2B+6%2A12%29
A = Pi+%28108%29
A = 339.28 sq cm