1954 AHSME Problems/Problem 27: Difference between revisions
Katzrockso (talk | contribs) Created page with "== Problem 27== A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that of the sphere. The ratio of..." |
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== Solution == | == Solution == | ||
Because the circle has the same radius as the sphere, the cylinder and sphere have the same radius. Then from the volume of cylinder formula, we have < | Because the circle has the same radius as the sphere, the cylinder and sphere have the same radius. Then from the volume of cylinder formula, we have <cmath>\frac{1}{3}\pi r^2 h= \frac{4}{6}\pi r^3 \implies h=2r</cmath> | ||
Revision as of 19:08, 14 April 2016
Problem 27
A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that of the sphere. The ratio of the altitude of the cone to the radius of its base is:
Solution
Because the circle has the same radius as the sphere, the cylinder and sphere have the same radius. Then from the volume of cylinder formula, we have ![\[\frac{1}{3}\pi r^2 h= \frac{4}{6}\pi r^3 \implies h=2r\]](http://latex.artofproblemsolving.com/b/b/0/bb006c9b95cd1deed75ffb72850579112552230d.png)
