Digging a rectangular prism for a pool. It is 42 ft * 29.5 ft * 8ft. The hauling truck holds 452.5 cubic feet away in a load. How many truckloads of dirt will have to be hauled away to finish the job?

Recall that the amount of dirt that the truck hauls away will equal the volume of the pool.

If the pool's dimensions are 42 ft x 29.5 ft x 8 ft

and Volume = base * width * height

we can denote the base as 42 ft, the width as 29.5 ft, and the height as 8 ft.

Pool volume = 42 * 29.5 * 8

Pool volume = 9,912 cubic ft

Therefore

Dirt volume = 9,912 cubic ft

Assume the hauling truck is at capacity with 425.5 cubic feet.

If we want to know how many truckloads will need to be taken away, and we know how the volume of the dirt that will need to be removed and how much a truck will hold, then we need to divide our total volume of dirt by the volume of dirt that one truck can carry.

Number of truckloads = 9,912 : 425.5

Number of truckloads = 23.295

Because the truck will still have extra after his 23rd haul, it will still have to make one last haul away, despite not being full.

We can then round up 23.295 truckloads to 24 truckloads.

The volume of the prism = 42 * 29.5 * 8

= 9912 ft^3

Number of truckloads needed = 9912 / 452.5

= 21.90

So the answer is 22 truckloads.