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 = $220\times 10^6g$

conversions used : 1 metric ton = 1000000 g

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

$Volume=\frac{Mass}{Density}$

$Volume=\frac{220\times 10^6g}{3.11g/cm^3}=7.07\times 10^7cm^3$

Convert cubic centimeter to cubic yard:

$1cm^3=1.30795\times 10^{-6}yards^3$

So,

Volume of load = $\frac{1.30795\times 10^{-6}yards^3}{1cm^3}\times (7.07\times 10^7cm^3)$

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