KöMaL 2016 C1331

Pete invited 13 friends to the party celebrating his 13th birthday. He received 13 coloured candles from each friend. The candles were right cylinders of radius 2.5 cm and height 30 cm. In order to keep his treasures safe, Pete has got hold of a large rectangular box of dimensions $\rm 50~cm \times 78~cm \times 31~cm$. Can he place all the candles in the box so that no candle should stick out of the box or be injured?