Question

1. the mass of fuel in an airplane must be determined before takeoff. a jet contains 155,211 l of fuel after it has been filled with fuel. what is the mass of the fuel in kilograms if the fuel’s density is 0.768 g/cm³?

Explanation:

Step1: Convert volume units

We know that \(1\space L = 1000\space cm^3\), so to convert \(155211\space L\) to \(cm^3\), we multiply by \(1000\).
\(155211\space L\times1000 = 155211000\space cm^3\)

Step2: Use density formula to find mass

The density formula is \(
ho=\frac{m}{V}\), where \(
ho\) is density, \(m\) is mass, and \(V\) is volume. Rearranging for mass, we get \(m =
ho\times V\).
Given \(
ho = 0.768\space g/cm^3\) and \(V = 155211000\space cm^3\), we calculate the mass in grams:
\(m = 0.768\space g/cm^3\times155211000\space cm^3 = 119202048\space g\)

Step3: Convert mass to kilograms

Since \(1\space kg = 1000\space g\), we divide the mass in grams by \(1000\) to get the mass in kilograms:
\(\frac{119202048\space g}{1000} = 119202.048\space kg\)

Answer:

\(119202.048\space kg\)