Using volume of a rectangular prism, it is found that the dump truck will have to make 266 trips to haul away all of the soil.
What is the volume of a rectangular prism?
The volume of a rectangular prism of length l, width w and height h is given by:
[tex]V = lwh[/tex]
In this problem, both the hole and the open-box bed are rectangular, hence the number of trips is the ratio between the volumes of the hole and of the open-box bed.
What is the volume of the volume of the hole?
The dimensions in meters are [tex]l = 11, w = 14.5, h = 4[/tex], hence:
[tex]V_h = 11(14.5)(4) = 638[/tex]
What is the volume of the volume of the open-box?
The dimensions in meters are [tex]l = 4, w = 3, h = 0.2[/tex], hence:
[tex]V_b = 4(3)(0.2) = 2.4[/tex]
What is the ratio of the volumes?
It's their division, hence:
[tex]r = \frac{V_h}{V_b} = \frac{638}{2.4} = 265.8[/tex]
Rounding up, the dump truck will have to make 266 trips to haul away all of the soil.
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