SOLUTION: If the surface area of a cone of radius 6m is 96 pi, find the volume of the cone

Algebra ->  Surface-area -> SOLUTION: If the surface area of a cone of radius 6m is 96 pi, find the volume of the cone      Log On


   

Question 981797: If the surface area of a cone of radius 6m is 96 pi, find the volume of the cone
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Surface Area of a cone =
pi x r^2 + pi x r x l
Surface Area = pir(r + l)
96pi/pi6 = 6 + l
16 = 6 + l
l (Slant height) = 10m
Using Pythagoras and a
right angled triangle
Hypotenuse = 10m
Base = 6m
To find height.
Height = √ 10^2 - 6^2
Height = √64
Volume of cone =
1/3 x pi x r^2 x h
1/3 x pi x 6^2 x √64
Volume = 301.6 m^3
Hope this helps:-)