document.write( "Question 1027792: A pile of coal has a rectangular base 50 ft. by 400 ft. If the sides of the pile are all inclined 45 degrees to the horizontal, and the coal weighs 94 lb. per cu. ft., find the number of tons of coal in the pile. \n" ); document.write( "

Algebra.Com's Answer #643007 by Cromlix(4381) $\"\"$ $\"About$

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Hi there,
\n" ); document.write( "Basically you have a rectangular
\n" ); document.write( "based pyramid.
\n" ); document.write( "Volume = 1/3 base area x height.
\n" ); document.write( "Base area = 50 x 400 = 20000ft^2
\n" ); document.write( "Height is found by:
\n" ); document.write( "Finding diagonal of base.
\n" ); document.write( "Diagonal^2 = length^2 + Base^2
\n" ); document.write( "Diagonal^2 = 400^2 + 50^2
\n" ); document.write( "Diagonal = √162500
\n" ); document.write( "Diagonal = 403.11ft
\n" ); document.write( "Halve 403.11ft = 201.56ft
\n" ); document.write( "Consider you have a right angled
\n" ); document.write( "triangle.
\n" ); document.write( "Base = 201.56
\n" ); document.write( "To find the height:
\n" ); document.write( "Angle between base and hypotenuse
\n" ); document.write( "= 45 degrees.
\n" ); document.write( "Using Tan(theta) = Opposite/Adjacent
\n" ); document.write( "tan(45) = Opposite/201.56
\n" ); document.write( "Opposite (Height) = tan(45) x 201.56
\n" ); document.write( "Height = 326.48ft.
\n" ); document.write( "Volume = 1/3 base area x height.
\n" ); document.write( "(Base area = 50 x 400 = 20000ft^2)
\n" ); document.write( "(Height = 326.48ft.)
\n" ); document.write( "Volume = 1/3 x 20000 x 326.48
\n" ); document.write( "Volume = 2176533.33ft^3
\n" ); document.write( "Weight = 94 x 2176533.33
\n" ); document.write( "= 204594133 lbs
\n" ); document.write( "= 102297.07 tons
\n" ); document.write( "Hope this helps :-) \n" ); document.write( "

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