Question

question 20 (5 points) \\ saved a batch of xenite has a density 4.15 g/ml. if the mass of the batch is 340 metric tons, how many dump trucks, each with a capacity of 18 cubic yards will be needed to haul the whole batch? round to the nearest integer. 1 yard = 91.44 cm 1 metric ton = 1000 kg \\ 7 trucks \\ 6 trucks \\ 8 trucks \\ 5 trucks \\ 4 trucks

Explanation:

Step1: Convert cubic yards to cubic centimeters

First, we know that 1 yard = 91.44 cm, so 1 cubic yard = (91.44 cm)³. Calculate the volume of 18 cubic yards:
Volume of 1 truck = \(18\times(91.44)^3\) cm³.
\((91.44)^3 = 91.44\times91.44\times91.44 \approx 763503.2\) cm³.
So 18 cubic yards = \(18\times763503.2 \approx 13743057.6\) cm³.

Step2: Convert volume to mass (in grams)

Density \(d = 4.15\) g/mL, and 1 cm³ = 1 mL. So mass of xenite per truck:
\(m = d\times V = 4.15\) g/mL \(\times13743057.6\) mL \(\approx 5.7033689\times10^7\) g.

Step3: Convert mass to metric tons

1 metric ton = 1000 kg = \(10^6\) g. So mass per truck in metric tons:
\(m_{ton} = \frac{5.7033689\times10^7\ \text{g}}{10^6\ \text{g/metric ton}} \approx 57.0337\) metric tons per truck.

Step4: Calculate number of trucks needed

Total mass of batch is 340 metric tons. Number of trucks \(n = \frac{340}{57.0337} \approx 5.96\), round to nearest integer is 6.

Answer:

6 trucks