Mass of flag to be lifted, M(x) = [∫ ∫ ( )

]

Centroid, y(x) =

( ) ( )

( )

; 0

= ( )

;

Work done for lifting the flag,

W = {∫

( ) ( )

( )

∫ ( ) [( )

]

}

L= 27.43

W=18.29

Rho* T = 0.075

W = 1807.6 Joules

Density of hot air, ρh =

Density of hot air, ρhe =

Density of outside air, ρ =

Mass to be lifted by the balloon, m =

Volume of the balloon =

Volume of the balloon =

Diameter of the balloon =