SOLUTION: The area of a circle is 3 1/7 times the square of the radius. Find weight of a circular disc of cast iron 7 ft. in diameter and 1 1/3 in. thickness. A plate of cast iron 1 ft

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Question 1129384: The area of a circle is 3 1/7 times the square of the radius. Find weight of a circular disc of cast iron 7 ft. in diameter and 1 1/3 in. thickness.
A plate of cast iron 1 ft. square and 1 in. thickness weighs 37.5 lbs.
Attempt:
The disc is a cylinder.
Volume; pi * r*2 * height. 3.1416 * 3.5 * 3.5 * .1108333 = 4.265375 cu. ft.
Not sure how to continue.
Found 3 solutions by josgarithmetic, josmiceli, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
That given 3%261%2F7 is an approximation for pi.

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Find weight of a circular disc of cast iron 7 ft. in diameter and 1 1/3 in. thickness.
A plate of cast iron 1 ft. square and 1 in. thickness weighs 37.5 lbs.
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pi%2Across%28%287%2F2%29%5E2%29%2A%281%261%2F3%29, cubic inches, the circular cast iron disc
No.. Not 7 inches diameter; but "7 feet diameter".


All the rest of this was wrong:
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The described PLATE of cast iron, density:
%2837.5%2Apounds%29%2F%2812%2Ainches%2A12%2Ainches%2A1%2Ainch%29

%2837.5%2F144%29%28pounds%2Fcubicinch%29



The weight of the circular cast iron disc:
%28pi%2A%287%2F2%29%5E2%2A%281%261%2F3%29%2837.5%2F144%29%2Apounds%29

You can compute the expression how you want.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find density of iron in pounds/cubic inch
Volume of iron plate:
+V+=+12%2A12%2A1+=+144+ in3
Density:
+37.5%2F144+=+.26042+ lbs/in3
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Find volume of circular disk
+V+=+%2822%2F7%29%2A42%5E2%2A%284%2F3%29+ in3
+V+=+%28+88%2F21+%29%2A1764+
+V+=+7392+ in3
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[ weight ] = [ density ] x [ volume ]
+W+=+.26042%2A7392+
+W+=+1925.025+ pounds
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Get a 2nd opinion if needed

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by tutor @josgarithmetic is not correct; he misread the given information about the weight of cast iron.

The given information is that a plate of cast iron 1 foot square and 1 inch thick weighs 37.5 pounds. Although it is unorthodox to do calculations in mixed units (square feet times inches), it is possible to do so if you pay attention to what you are doing.

The volume of the given cylindrical disk is

%28pi%29%28r%5E2%29%28h%29+=+%2822%2F7%29%283.5%5E2%29%284%2F3%29 in units of square feet times inches.

Then, since the given information about the weight of cast iron is in those same mixed units, the weight of the disk is

%2822%2F7%29%283.5%5E2%29%284%2F3%29%2837.5%29+=+1925