SOLUTION: The surface area of a right cone is 400.2 m^2. The radius of the cone is 6.0m. Determine the height of the cone to the nearest metre.

Algebra ->  Surface-area -> SOLUTION: The surface area of a right cone is 400.2 m^2. The radius of the cone is 6.0m. Determine the height of the cone to the nearest metre.      Log On


   

Question 1079630: The surface area of a right cone is 400.2 m^2. The radius of the cone is 6.0m. Determine the height of the cone to the nearest metre.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The surface area of a right cone is 400.2 m^2. The radius of the cone is 6.0m. Determine the height of the cone to the nearest metre.
:
Surface Area of a cone: S.A. = %28pi%2Ar%2As%29+%2B+%28pi%2Ar%5E2%29 where:
r = the radius
s = the slant height
:
Find the s
%28pi%2Ar%2As%29+%2B+%28pi%2A6%5E2%29 = 400.2
divide thru by pi
%286%2As%29+%2B+%286%5E2%29 = 127.3876
6s = 127.324 - 36
6s = 91.3876
s = 91.3876/6
s = 15.23 meter is the slant height
find the height using pythag; h^2 = 15.23^2 - 6^2 (h is the hypotenuse)
h = sqrt%2815.23%5E2+-+36%5E2%29
h = 14 meters is the height