Difference between revisions of "1954 AHSME Problems/Problem 27"
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...") |
Katzrockso (talk | contribs) (→Solution) |
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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