The lateral area of a right circular cone is 20pi cm^2 and the total area is 36pi cm^2 find the volume of the cone

Let r = radius, h = height and l = slant height 

Lateral area = rlpi 

But l = sqrt(r^2 + h^2) 

Lateral area = r sqrt( r^2 + h^2) pi = 20 pi(1) 

Total area = r sqrt( r^2 + h^2) pi + r^2 pi = 36pi(2) 

Subtract (1) from (2) 

r^2 pi = 16 pi 

r^2 = 16 

r = 4 cm 

Put this value in (1) to find h 

4sqrt(4^2 + h^2) pi = 20 pi 

sqrt(16 + h^2) = 5 

Square both sides 

16 + h^2 = 25 

h^2 = 9 

h = 3 cm 

Now that we know h and r we can find the volume 

V = 1/3 pi r^2 h 

= 1/3 pi (4^2)(3) 

= 16 pi cm^3 ( = 50.27 cm^3)

I hope my answer has come to your help. God bless and have a nice day ahead!

Hello there.

The lateral area of a right circular cone is 20pi cm^2 and the total area is 36pi cm^2 find the volume of the cone

 50.27 cm^3