SOLUTION: The lateral area of a right circular cone is 416.27 cm² .Its altitude is 2/3 of its radius. Determine the radius of the cone.

Algebra ->  Trigonometry-basics -> SOLUTION: The lateral area of a right circular cone is 416.27 cm² .Its altitude is 2/3 of its radius. Determine the radius of the cone.      Log On


   

Question 1085023: The lateral area of a right circular cone is 416.27 cm² .Its altitude is 2/3 of its radius. Determine the radius of the cone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let r = the radius of the cone
then
2%2F3r = the height of the cone
:
Area formula A = pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29
pi%2Ar%2Asqrt%28r%5E2%2B%28%282%2F3%29r%29%5E2%29 = 416.27
pi%2Ar%2Asqrt%28r%5E2%2B%284%2F9%29r%5E2%29 = 416.27
pi%2Ar%2Asqrt%28%2813%2F9%29r%5E2%29 = 416.27
extract the squares
%28%28pi%2Ar%5E2%29%2F3%29%2Asqrt%2813%29 = 416.27
multiply both sides by 3
pi%2Ar%5E2%2Asqrt%2813%29 = 1248.81
divide both sides by the sq root of 13
pi%2Ar%5E2+=+346.3576
divide both sides by pi
r^2 = 110.25
r = sqrt%28110.25%29
r = 10.5 cm is the radius of the cone