Question

A transport company needs to deliver 300 pounds of rocks to a construction site. The company owns a set of dump trucks- each with a container in the shape of a rectangular prism (figure A). If each pound of rock has a mass of 8 cubic feet, how many dump trucks will it take to transport the rock?

Calculate the total volume of rock that the transport company is responsible for.
Calculate the maximum volume of each dump truck.
How many trucks are needed to deliver the rock in one trip?

Answer 1

Given:

Weight of rocks to be delivered = 300 pounds

Mass of each rock = 8 cubic feet

Height of each dump truck = 8 ft

Length of each dump truck = 12 ft

Width of each dump truck = 9ft

Let's solve for the following:

• a) Calculate the total volume of rock that the transport comapny is responsible for.

To find the total volume of rock, apply the formula below:

Total volume = (Weight of rocks to be delivered) x (Mass of each rock)

Thus, we have:

Total volume = 300 x 8 = 2400 cubic feet

Therefore, the total volume of rock the transport company is responsible for is 2400 cubic feet.

• b) Calculate the maximum volume of each dump truck.

Since the dump truck has the shape of a rectangular prism, to find the maximum volume of each dump truck apply the formula for the volume of a rectangular prism.

Volume = Length x Width x Height

Thus, we have:

Volume = 12 x 9 x 8 = 864 cubic feet

Therefore, the maximum volume of each dump truck is 864 cubic feet.

• c) How many trucks are needed to deliver the rock in one trip.

To find the number of trucks needed in one trip, apply the formula below:

`\text{Number of trucks = }\frac{Total\text{ volume of rock}}{\max imum\text{ volume of each dump truck}}`

Thus, we have:

`\text{Number of trucks = }\frac{2400^{}}{864}=2.78\approx3`

Therefore, approximately 3 trucks are needed to deliver the rock in one trip

ANSWER:

• a) 2400 cubic feet

,

• b) 864 cubic feet

,

• c) 3 trucks