Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 233. (December 2009)

K. 233. Mr. Bear's favourite honey jar is a right circular cylinder of diameter 16 cm. His favourite spoon is 23 cm long, he normally eats honey with that spoon. One day Mr. Bear accidentally dropped the spoon into the jar, and it submerged totally in the honey. What was the minimum possible amount of honey in the jar? (Ignore the volume of the spoon.)

(6 pont)

Deadline expired on January 11, 2010.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Amikor a kanál beleesik a csupurba, akkor ``keresztben'' fog megállni: a kanál egy derékszögű háromszög átfogóját adja, aminek egyik befogója a csupor aljának egyik átmérője. Pithagoras tétele szerint \(\displaystyle 23^2=16^2 + h^2\), ha a kanál teteje a csupor aljától \(\displaystyle h\) magasságban van. Ekkor \(\displaystyle h=\sqrt{273}\approx 16,52271\ cm\). A méznek legalább \(\displaystyle h\) magasságig kell érni, hogy a kanál elmerüljön teljesen, ekkor a térfogata \(\displaystyle \left(\frac{16} 2\right)^2 \cdot \pi \cdot h \approx 3320,404\ cm^3 \approx 3,3204\ dm^3\). Legalább kb. \(\displaystyle 3,321\ l\) méznek kell lennie a csuporban.


Statistics:

210 students sent a solution.
6 points:52 students.
5 points:90 students.
4 points:13 students.
3 points:5 students.
2 points:5 students.
1 point:38 students.
0 point:3 students.
Unfair, not evaluated:4 solutions.

Problems in Mathematics of KöMaL, December 2009