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.
<h3>What is the volume of a rectangular prism?</h3>
The volume of a rectangular prism of length l, width w and height h is given by:
![V = lwh](https://tex.z-dn.net/?f=V%20%3D%20lwh)
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.
<h3>What is the volume of the volume of the hole?</h3>
The dimensions in meters are
, hence:
![V_h = 11(14.5)(4) = 638](https://tex.z-dn.net/?f=V_h%20%3D%2011%2814.5%29%284%29%20%3D%20638)
<h3>What is the volume of the volume of the open-box?</h3>
The dimensions in meters are
, hence:
![V_b = 4(3)(0.2) = 2.4](https://tex.z-dn.net/?f=V_b%20%3D%204%283%29%280.2%29%20%3D%202.4)
<h3>What is the ratio of the volumes?</h3>
It's their division, hence:
![r = \frac{V_h}{V_b} = \frac{638}{2.4} = 265.8](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7BV_h%7D%7BV_b%7D%20%3D%20%5Cfrac%7B638%7D%7B2.4%7D%20%3D%20265.8)
Rounding up, the dump truck will have to make 266 trips to haul away all of the soil.
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