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## Problem

The density of air is $1.29 \: kg/m^3$ and the density of helium is $0.18 \: kg/m^3$. The mass of the balloon is $20 \: kg$.

What volume of helium would a hot air balloon needed to lift a $180 \: kg$ crate?

## Solution

The balloon must be able to lift the crate and its own mass.

$F_B = ({m}_{He} + 180 + 20)g$
${\rho}_{air} Vg = \left({\rho}_{He} V + 200 \right) g$
$V = \frac{200}{{\rho}_{air} - {\rho}_{He}}$
$V = \frac{200}{1.29 - 0.18}$
$V = 180 \: m^3$
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