SOLUTION: The volume of a cone having an inclined axis at an angle of 60 degrees with the base is equal to 1884.96 cu.m., find the length of the axis of the cone, if the radius at the base 1

Algebra ->  Bodies-in-space -> SOLUTION: The volume of a cone having an inclined axis at an angle of 60 degrees with the base is equal to 1884.96 cu.m., find the length of the axis of the cone, if the radius at the base 1      Log On


   

Question 891676: The volume of a cone having an inclined axis at an angle of 60 degrees with the base is equal to 1884.96 cu.m., find the length of the axis of the cone, if the radius at the base 10m.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a cone having an inclined axis at an angle of 60 degrees with the
base is equal to 1884.96 cu.m., find the length of the axis of the cone, if the
radius at the base 10m.

 

Let A be the axis of the red cone. The green cone has the same 
vertical height as the red slanted cone and has the same volume.

The volume of the green cone is

V=expr%281%2F3%29pi%2Ar%5E2h

1884.96=expr%281%2F3%29pi%2810%29%5E2h

1884.96%2F%28expr%281%2F3%29pi%2810%29%5E2%29=h

18.00004209=h

We'll just round that to 18m.

h%2FA=sin%28%2260%B0%22%29

18=Asin%28%2260%B0%22%29

18%2Fsin%28%2260%B0%22%29=A

20.78460969=A

So the axis is about 20.8 m

Edwin