A machine bales recycled goods into bales measuring 5ft by 4ft by 3ft.
a) a new machine is beign considered that will make right cylindrical bales. If the bales contain the same amount of materal as the original ones and have a height of 5ft, what is their diameter?
b) Which type of bale has a smaller surface area? Justify your answer
+130536 A machine bales recycled goods into bales measuring 5ft by 4ft by 3ft.
a) a new machine is beign considered that will make right cylindrical bales. If the bales contain the same amount of materal as the original ones and have a height of 5ft, what is their diameter?
b) Which type of bale has a smaller surface area? Justify your answer
a) The volume of each bale produced by the first baler is 60ft^3
Vcylinder = pi r^2 * h ....so we have
60ft^3 = pi * r^2 * 5ft
[60 ft^3] / [ 5 pi ft ] = r^2 take the square root of each side
r ≈ 1.95 ft so the diameter ≈ 3.90 ft
b) the surface area of the first bale = 2 [20 + 15 + 12] = 2 [ 47] = 94 ft^2
The surface area of the cylindrical bale = 2pi * r (r + h) = 2pi* 1.95 (1.95 + 5) ≈ 85.15 ft^2
So....the cylindrical bale has the smaller surface area......
