Question

A load of bauxite has a density of 3.11 . If the mass of the load is 220. metric tons, how many dump trucks, each with a capacity of 11 cubic yards, will be needed to haul the whole load? (Express your answer as an integer.)

Answer 1

Answer : The number of dump trucks required are, 8

Explanation : Given,

Density of load of bauxite =
`3.11g/cm^3`

Mass of load = 220 metric tons =
`220* 10^6g`

conversions used : 1 metric ton = 1000000 g

First w have to calculate the volume of load of bauxite.

`Volume=(Mass)/(Density)`

`Volume=(220* 10^6g)/(3.11g/cm^3)=7.07* 10^7cm^3`

Convert cubic centimeter to cubic yard:

`1cm^3=1.30795* 10^(-6)yards^3`

So,

Volume of load =
`(1.30795* 10^(-6)yards^3)/(1cm^3)* (7.07* 10^7cm^3)`

Volume of load = 92.47 cubic yards

Now we have to calculate the number of dump trucks.

Capacity of a dump truck = 11 cubic yard

Number of trump trucks required =
`\frac{92.47\text{ cubic yard}}{11\text {cubic yard}}=8.406\approx 8`

Thus, the number of dump trucks required are, 8