Question

select the correct answer. the volume of helium in a blimp is 6.28×10^9 milliliters. the density of helium in the blimp is 0.1786 $\frac{kilogram}{meter^3}$. find the mass of the helium in the blimp (hint: 1,000 l = 1 cubic meter.) a. 1,120 kg b. 1.12 kg c. 3.52×10^7 kg d. 2,840 kg

Explanation:

Step1: Convert volume to cubic - meters

Since \(1\ L = 1000\ mL\) and \(1\ m^{3}=1000\ L\), then \(1\ m^{3}=10^{6}\ mL\). Given \(V = 6.28\times10^{9}\ mL\), so \(V=\frac{6.28\times 10^{9}}{10^{6}}m^{3}=6.28\times10^{3}m^{3}\).

Step2: Use the density - mass formula

The density formula is \(
ho=\frac{m}{V}\), where \(
ho\) is density, \(m\) is mass, and \(V\) is volume. Rearranging for \(m\) gives \(m =
ho V\). Given \(
ho=0.1786\frac{kg}{m^{3}}\) and \(V = 6.28\times10^{3}m^{3}\), then \(m=0.1786\times6.28\times 10^{3}kg\).
\(m=(0.1786\times6.28)\times10^{3}kg\approx1.12\times10^{3}kg = 1120kg\).

Answer:

A. \(1,120\ kg\)