Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 894. (March 2007)

C. 894. A hemispherical soup bowl has a volume of 8 litres. How much soup will fill the bowl to half its height?

(5 pont)

Deadline expired on April 16, 2007.

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


8~{\rm l}=8~{\rm dm}^3=2/3\,{\rm r}^3\pi,

ahonnan r3=12/\pi dm3.

A gömbszelet térfogata:

V=\pi/3.(r/2)2(3r-r/2)=\pi/3(3 r3/4-r3/8)=2,5 dm3=2,5 l.


315 students sent a solution.
5 points:208 students.
4 points:55 students.
3 points:18 students.
2 points:9 students.
1 point:1 student.
0 point:2 students.
Unfair, not evaluated:22 solutions.

Problems in Mathematics of KöMaL, March 2007