SOLUTION: The radii of two similar cones are in the ratio 5:3.Find the ratio of their volumes

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The radii of two similar cones are in the ratio 5:3.Find the ratio of their volumes      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 915396: The radii of two similar cones are in the ratio 5:3.Find the ratio of their volumes
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
They are similar, so the heights are in the same ratio.

The ratio for radius of larger to smaller cone is 5%2F3;
and because of the two cones being SIMILAR, the ratio of the HEIGHT of the larger cone to the smaller cone is also 5%2F3.



smaller 3r, 3h
larger, 5r, 5h
Using v for volume of smaller and V for volume or larger,
v=%281%2F3%29%283h%29%28pi%29%283r%29%5E2 and V=%281%2F3%29%285h%29%28pi%29%285r%29%5E2.

You can calculate V%2Fv, the ratio of the volume of the larger cone to the volume of the smaller cone. Substitute the expressions:



Simplify that ratio.