SOLUTION: The inside radius of a spherical metal shell is 50cm and the thickness of the shell is 0.4cm. Calculate the volume of the material used in the shell to the nearest unit. The fo

Algebra ->  Volume -> SOLUTION: The inside radius of a spherical metal shell is 50cm and the thickness of the shell is 0.4cm. Calculate the volume of the material used in the shell to the nearest unit. The fo      Log On


   

Question 152758: The inside radius of a spherical metal shell is 50cm and the thickness of the shell is 0.4cm. Calculate the volume of the material used in the shell to the nearest unit.
The formula for volume of a sphere is 4/3 pi r^3 so is the answer 4/3 pi 50^3 = 523333.33 or do I have to do something with the 0.4cm thickness?
Thanks
Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The inside radius of a spherical metal shell is 50cm and the thickness of the shell is 0.4cm. Calculate the volume of the material used in the shell to the nearest unit.
The formula for volume of a sphere is 4/3 pi r^3 so is the answer 4/3 pi 50^3 = 523333.33 or do I have to do something with the 0.4cm thickness?
Thanks
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Calculate the total volum of the sphere, then subtract the volume of a sphere 0.4 cm smaller radius.
Vol of material = 4%2API%2A50.4%5E3%2F3+-+4%2API%2A50%5E3%2F3
= %284%2API%2F3%29%2A%2850.4%5E3+-+50%5E3%29
= 12,667 cc (cubic cm)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You need to find the volume of the outer sphere (V%5B2%5D)and subtract the volume of the inner sphere (V%5B1%5D):
V%5B2%5D+=+%284%2F3%29%2Api%2AR%5B2%5D%5E3 - V%5B1%5D+=+%284%2F3%29%2Api%2AR%5B1%5D%5E3
V%5B2%5D+=+%284%2F3%29%2Api%2A%2850.4%29%5E3 - V%5B1%5D+=+%284%2F3%29%2Api%2850%29%5E3
V%5B2%5D+=+4.2%28128024.064%29 - V%5B1%5D+=+4.2%28125000%29 = 4.2%283024.064%29+=+highlight%2812701%29 cu.cm Approximately.