Problem C. 869. (October 2006)
C. 869. A cylinder of height is inscribed into a sphere of radius R. Determine the ratio of their volumes.
(5 pont)
Deadline expired on November 15, 2006.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. Jelöljük R-rel a gömb, r-rel a henger sugarát, és m-mel a henger magasságát.
Ekkor az ábra alapján a Pitagorasz-tételt felírva:
ahonnan
A térfogatok aránya innen
Tehát a henger a gömb térfogatának -része.
Statistics:
570 students sent a solution. 5 points: 451 students. 4 points: 53 students. 3 points: 18 students. 2 points: 23 students. 1 point: 6 students. 0 point: 11 students. Unfair, not evaluated: 8 solutionss.
Problems in Mathematics of KöMaL, October 2006