SOLUTION: a cone is inscribed in a cylindrical container that can hold 5555 liters of water. What would be the slant height of the cone if its vertex lie on the top of the surface of the cyl

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a cone is inscribed in a cylindrical container that can hold 5555 liters of water. What would be the slant height of the cone if its vertex lie on the top of the surface of the cyl      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 971902: a cone is inscribed in a cylindrical container that can hold 5555 liters of water. What would be the slant height of the cone if its vertex lie on the top of the surface of the cylindrical container? The base of the cylindrical container is also the base of the cone with 0.05 meter radius.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
h, the height of both the cone and the cylinder; not yet at the slant height.
h%2Api%2A%28.05%2A100%29%5E2=5555%2A1000, unit for h is in centimeters.

h=5555%2A1000%2F%28pi%2A%280.05%2A100%29%5E2%29
highlight_green%28h=70728%29, centimeters.

call this 70.728 METERS for now.

The slant height becomes a hypotenuse of right triangle with 0.05 meter and 70.728 meter legs.
If s is slant height, then 0.05%5E2%2B70.728%5E2=s%5E2
highlight%28s=sqrt%280.05%5E2%2B70.728%5E2%29%29
and this can be simplified or computed.