Solve Buoyancy Problem: Estimate Balloon Radius for 6 Yr Old Boy

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To estimate the radius of a helium balloon that can lift a 25 kg boy, the buoyancy force must exceed the boy's weight. The volume of the balloon is calculated using the formula V=(4/3)*pi*r^3. The buoyancy force is determined by the difference in density between air and helium, with air density at approximately 1.25 kg/m3 and helium at 0.180 kg/m3. After initial uncertainty, the poster confirmed they found a solution to the problem. The discussion highlights the importance of buoyancy calculations in determining the necessary balloon size.
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Homework Statement


A six year old boy weights about 25 kg. Estimate the radius of a spherical helium balloon capable of lifting the boy.Solution 2.

Homework Equations



V=(4/3)*pi*r^3.

B= density of air* volume *g if in air

The Attempt at a Solution



the buoyancy must be greater than the weight.
Density of helium is 4g/22.4l = 0.180 kg/m3.
Density of air (Nitrogen) is 28g/22.4l = 1.25 kg/m3.


not sure where to go from here...

thanks
 
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