SOLUTION: An iron ball 9 in. diameter weighs 14 lb. Find the weight of an iron shell 2 in. thick whose external diameter is 20 in.

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Question 1194334: An iron ball 9 in. diameter weighs 14 lb. Find the weight of an iron shell 2 in. thick whose external diameter is 20 in.
Found 3 solutions by josgarithmetic, ikleyn, Alan3354:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
outter dimension volume
inner dimension volume (empty),

shell volume,
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

Solve the problem in 3 steps. 

(1)  Find the density of iron by dividing the weight of the sphere 9 inches of diameter by its volume.


     Check the value of the iron density, which you get, with the standard value from the tables.
     If it is close, continue your calculations in steps 2 and 3.
     If it is not close, stop your calculations, since the input is incorrect.


(2)  Find the volume of metal of the second hollow sphere as the difference of the outer and interior volumes.


(3)  Find the density of the hollow sphere multiplying the metal volume by the iron density.

Happy calculations (!)


//////////////


Regarding the post by @josgarithmetic, where he proposes to use for 

 
    VOLUME of the shell,


you better  IGNORE  it for your safety,  since his formula is  TOTALLY  WRONG  and  IRRELEVANT.


Use the correct formula for the volume of this shell 

    V =  =  = 2044.128 cubic inches.

I am sure you know it,  since this knowledge is a necessary pre-requisite for solving this problem.


\\\\\\\\\\\\\\\\


After seeing my post, @josgarithmetic erased his writing, and it is good: it means that my notice was not wasted.

At least, feature readers will be spared of seeing that gibberish.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
An iron ball 9" in diameter would weigh ~108.4 pounds.
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