# Fluids - floating balloon problem

Hi - I know this must be a basic question, but I'm doing this physics problem and I can't get the exact answer!

Here it is and my work along with it - can someone please tell me what I'm missing in my equations?

The problem is taken from the James Walker physics book - Chapter 15. Number 29.

A 0.12 kg balloon is filled with helium (density = .179 kg/m-cubed).
The balloon is a sphere with radius of 5.2 m. What is the maximum
weight the baloon can lift?

I keep getting something close to 6.4 kN, whereas the book says 5.7 kN.

My work:

volume of baloon (which is actually the volume of helium) = 4/3 pi
r-cubed = 588.9 m-cubed

bouyance force lifts the balloon upward, while the weight of the
balloon, the weight of the helium and the weight of the unknown weight
(ex. block) counteracts the bouyance force.

Bouyance force = (density of air) (g) (V) = (1.29) (9.8) (588.9) =
7453 N (upward force)

Weight total = weight of baloon material + (density of helium) (g) (V)
+ unknown weight = (.12)(9.81) + (.179)(9.81)(588.9) + unknown weight
= bouyance force

this would make the unknown weight = 6.4 kN

Not 5.7 kN

Please someone help? Thanks a bunch!