SOLUTION: 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 num

Algebra ->  Bodies-in-space -> SOLUTION: 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 num      Log On


   

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.
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Basically you have a rectangular
based pyramid.
Volume = 1/3 base area x height.
Base area = 50 x 400 = 20000ft^2
Height is found by:
Finding diagonal of base.
Diagonal^2 = length^2 + Base^2
Diagonal^2 = 400^2 + 50^2
Diagonal = √162500
Diagonal = 403.11ft
Halve 403.11ft = 201.56ft
Consider you have a right angled
triangle.
Base = 201.56
To find the height:
Angle between base and hypotenuse
= 45 degrees.
Using Tan(theta) = Opposite/Adjacent
tan(45) = Opposite/201.56
Opposite (Height) = tan(45) x 201.56
Height = 326.48ft.
Volume = 1/3 base area x height.
(Base area = 50 x 400 = 20000ft^2)
(Height = 326.48ft.)
Volume = 1/3 x 20000 x 326.48
Volume = 2176533.33ft^3
Weight = 94 x 2176533.33
= 204594133 lbs
= 102297.07 tons
Hope this helps :-)