finding the total weight...

May 2012
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a concrete surge chamber with circular cone cross section and vertical inner walls has an inside diameter of 100 ft. the outer walls taper uniformly 1/2 in. to 1 ft. of rise, and at the base the thickness is 5 ft. the height of the surge chamber is 150 ft. above the pressure tunnel, and the material used in its construction weighs 159 lb. per cu. ft. find the total weight of the chamber when full of water.

answer = 49,352 short tons. (but i need to know how to come to this answer. thanks!)
 
Feb 2010
324
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How did you come up with these answers?

Have you attempted the problem?
 
Jul 2010
12,211
522
St. Augustine, FL., U.S.A.'s oldest city
The volume of a circular cone frustum is:

\(\displaystyle V=\frac{\pi h}{3}\(R_1^2+R_2^2+R_1 R_2\)\)

However, there is too much tapering of the wall. The thickness at the base is 60 in, and it tapers 150·0.5 in = 75 in.
 

Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
Just about the most confusingly worded problem I've seen;
can you not at least provide a diagram?
Does the fact that water weighs ~62.42796 pounds per cubic feet have anything to do with this?
How is the volume of the "construction material" suppose to be calculated?
 
May 2012
17
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FreaKariDunk said:
How did you come up with these answers?

Have you attempted the problem?
no, the answer for this problem was actually given at the back of the book where i've gotten the problem.. so yeah..