Answer:
9) 630 ft^3; 6.25 ft^3; 2 trucks (3, if you consider space utilization)
10) 71 m^3; 4 persons; no
Step-by-step explanation:
9) The volume of the truck is the product of the dimensions:
V = LWH = (15 ft)(7 ft)(6 ft) = 630 ft^3 . . . truck V
Likewise, the volume of a storage box is the product of its dimensions:
V = LWH = (2 ft)(2.5 ft)(1.25 ft) = 6.25 ft^3 . . . box V
If the boxes pack well into the truck (they don't), then the number of boxes that would fit in the truck is the ratio of these volumes:
number of boxes = (630 ft^3)/(6.25 ft^3) = 100.8
This suggests that half of the 200 boxes will fit in one truck, so 2 trucks are needed.
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Comment on space utilization
In the real world, not all of the truck's interior space can be utilized. This is because not all of the truck dimensions are integer multiples of the box dimensions. 96 is about the most boxes that can be placed in the truck. (Fitting more than 90 requires boxes be first layered one way, then layered another way to fill as much of the remaining space as possible.) In the real world, 3 trucks are needed to move 200 of these boxes.
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10) The area of the end triangle of the chalet is ...
A = (1/2)bh = (1/2)(5 m)(7.1 m) = 17.75 m^2
Then the volume of the chalet is ...
V = Bh = (17.75 m^2)(4 m) = 71 m^3 . . . volume of the chalet
At 15 m^3 per person, there is enough volume for ...
(71 m^3)/(15 m^3/person) = 4.73 persons
4 persons can stay in the chalet.
No, the entire family cannot stay in the chalet.
