SOLUTION: Hello, tutors, I have a problem. a spherical weather balloon needs to hold at least 175 cubic feet of helium to be buoyant enough to lift the meteorogical instruments. will a h

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Question 357126: Hello, tutors,
I have a problem.
a spherical weather balloon needs to hold at least 175 cubic feet of helium to be buoyant enough to lift the meteorogical instruments. will a helium-filled balloon with a diameter of 8 feet stay aloft?
What should I solve this problem? The volume? Please let me know the process about this.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's find the actual approximate volume of the sphere with a diameter of 8 ft. Since the diameter is 8 feet, the radius is r=d%2F2=8%2F2=4 feet. So r=4


V=%284%2F3%29pi%2Ar%5E3 Start with the volume of a sphere formula.


V=%284%2F3%29pi%2A%284%29%5E3 Plug in r=4.


V=%284%2F3%29%283.14159265%29%2A%284%29%5E3 Replace pi with 3.14159265 (note: Use more digits of pi to get better accuracy).


V=%284%2F3%29%283.14159265%29%2A%2864%29 Cube 4 to get 64.


V=%284%2F3%29%28201.0619296%29 Multiply 3.14159265 and 64 to get 201.0619296 (this figure is approximate).


V=268.0825728 Multiply 4%2F3 and 201.0619296 to get 268.0825728 (again, this figure is approximate).


So the approximate volume is 268.0825728 cubic feet which is definitely larger than 175 cubic feet.


So the balloon will stay aloft.