030 Review Problem - Amount of molten glass in a lump

Problem 30
Window glass formerly was made by gathering a lump of molten glass on the end of a hollow rod and blowing it into the form of large hollow cylinder about 6 ft. long and 1-1/2 ft. in diameter. This was cut longitudinally and then placed in an oven and heated until it softened, when it was flattened out into plates and cut into desired sizes. If this plate was 0.12 in. thick, find the amount of glass in the original lump.
 

Solution 30

 
ISAGANI HERNANDEZ

considering the volume of triangular prisms, when the hollow cylinder is stretch in horizontal layer, after cutting longituninally, will make the solution incorrect. The cross-section of the base, B will become trapezoidal not rectangular

Jhun Vert
Jhun Vert's picture

The hollow cylinder is actually very thin in comparison to its diameter. The error you mentioned is actually too small to include in calculation.

ISAGANI HERNANDEZ

Hi! Rommel I got the idea...see my other comment.....since this is solid geometry, guided by formula and justified by figure, whether the unit is too small if accuracy is needed, you cannot deny the correct solution.. what if we use km as the unit...anyway...I had answered the whole book in solid mensuration when I was in the college of civil engineering, the knowledge of solid geometry help be to become efficient estimator...HAVE A NICE DAY

Jhun Vert
Jhun Vert's picture

Thanks Isagani for your feedback. Maybe I will also show the solution you suggest if I've got the time to do it. Not by this time though.

ISAGANI HERNANDEZ

the circumference of inner diameter is not similar to the circumference of outside diameter, for this reason, it cannot be considered as rectangular prism and the base to be considered is trapezoidal...

ISAGANI HERNANDEZ

ok, I got the idea.....you consider the diameter, as the average or middle diameter of the hollow cylinder....since it falls on the middle, the answer could be correct

Jhun Vert
Jhun Vert's picture

The problem did not specify if the diameter is inner or outer. The solution above took the given diameter as the nominal diameter. How is the result of your calculations compared to the value of the result above? I suspect it is very small but I might be wrong because of the length. I did not verify it yet.

ISAGANI HERNANDEZ

I will send you my solution now if you will give me your e-mail..I am free now

Jhun Vert
Jhun Vert's picture

You can actually post it here as a comment. You can take a picture of your work and upload it in the comment.

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