Q1. A glass crystal sculpture is made in the shape of a regular octagonal prism with 10 cm sides. Each of the lateral faces is square. To avoid breakage in shipment, the piece is padded with plastic foam beads when it is packed in its square-based rectangular box. The layer of beads must be at least 1 cm thick on all sides of the glass including the top and bottom.
a) What is the minimum volume of beads required to protect the piece?
b) If the object was packed in a cylindrical container instead of a rectangular box, how would the minimum volume of beads change?
Q2. During a portage, the leader of a scout troop decided to save time by hiking around a wooded area between the base camp and a lake. The troop reached the lake by walking for 30 minutes on a bearing of N60degreesE, then for 45 minutes on a bearing of N80degreesW.
a) The leader figured that they walked at an average speed of 3 km/h. If they could have walked straight through the forested area at 1km/h, did the troop save any time by going around? If so, how much?
Two word problems are solved. The solution is detailed and well presented.