Mathematical and Physical Journal
for High Schools
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# Problem B. 4748. (November 2015)

B. 4748. A triangle $\displaystyle \mathcal H$ is rotated about a line lying in its plane but not intersecting it. Show that the volume of the resulting solid equals the product of the area of $\displaystyle \mathcal H$ and the perimeter of the circle described by the centroid of $\displaystyle \mathcal H$ during the rotation.

(5 pont)

Deadline expired on December 10, 2015.

### Statistics:

 68 students sent a solution. 5 points: Andó Angelika, Barabás Ábel, Baran Zsuzsanna, Borbényi Márton, Bukva Balázs, Busa 423 Máté, Csahók Tímea, Cseh Kristóf, Csorba Benjámin, Czirkos Angéla, Döbröntei Dávid Bence, Fekete Balázs Attila, Fülöp Anna Tácia, Gáspár Attila, Hansel Soma, Harsányi Benedek, Horváth András János, Imolay András, Kerekes Anna, Klász Viktória, Kocsis Júlia, Kocsis-Savanya Miklós, Kovács 162 Viktória, Kovács 246 Benedek, Lajkó Kálmán, Lakatos Ádám, Matolcsi Dávid, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Nagy Nándor, Németh 123 Balázs, Nguyen Viet Hung, Pálfy Máté András, Paulovics Péter, Polgár Márton, Radnai Bálint, Sal Kristóf, Schrettner Bálint, Souly Alexandra, Szécsényi Nándor, Tóth 2 Rudolf, Tóth Viktor, Vághy Mihály, Váli Benedek, Varjas István Péter, Várkonyi Dorka. 4 points: 13 students. 3 points: 4 students. 2 points: 1 student. 1 point: 2 students. 0 point: 2 students.

Problems in Mathematics of KöMaL, November 2015