SOLUTION: a mass weighs 125 grams and it is in a cylinder that measures 2.48" diameter and a length of 1.00" how do you calculate the pounds per square foot.

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Question 162700: a mass weighs 125 grams and it is in a cylinder that measures 2.48" diameter and
a length of 1.00" how do you calculate the pounds per square foot.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
you can translate inches to feet and grams to pounds first, or you can solve the problem and translate inches to feet and grams to pounds later.
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i will solve the problem in inches and grams first and then translate to pounds and feet after i get the result.
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mass is 125 grams in the shape of a cylinder.
volume of cylinder is pi*r^2*h
diameter = 2.48 inches
radius = 1/2 * diameter = 1.24 inches.
height of the cylinder is 1 inch.
let r = radius of the cylinder
let h = height of the cylinder
let pi = the constant 3.141592654
let V = volume of the cylinder
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first find the volume of the cylinder.
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V = pi*r^2*h
height (h) = 1 inch.
radius (r) = 1.24 inches.
formula becomes

V = pi*1.5376*1
V = 4.830512864 cubic inches.
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next find the grams per cubic inch.
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125 grams / 4.830512864 cubic inches = 25.87716947 grams per cubic inch.
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if the problem had asked you for grams per cubic inch you would be done.
unfortunately, the problem asked for pounds per cubic foot.
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actually, the problem asked for pounds per square foot, but this is wrong. the answer has to be in pounds per cubic foot since we are dealing with the volume of a cylinder which is expressed as a cubic measure.
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you divide the number of cubic inches by 1728 to get cubic feet.
(volume of 1 cubic foot is 1 foot * 1 foot * 1 foot which is the same as 12 inches * 12 inches * 12 inches = 1728 cubic inches.
1728 cubic inches is the same as 1 cubic foot.
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since there are 453.592 grams per pound, you divide the number of grams by 453.592 to get the number of pounds.
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125 grams / 453.592 grams per pound = .275578053 pounds.
4.830512864 cubic inches / 1728 = .002795436 cubic feet.
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.275578053 pounds / .002795436 cubic feet = 98.58143186 pounds per cubic foot.
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this becomes 98.58 pounds per cubic foot to the nearest hundredth of a pound per cubic foot.
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i didn't do any rounding and used values stored in the calculator rather than values displayed on the calculator. the answer will be slightly different if you use values displayed on the calculator rather than values stored in the calculator. for example, i did the calculations using the displayed values and the answer was 98.48... rather than the 98.58.... shown above.
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