Answer:
1357.7 m
Step-by-step explanation:
The cable has a circular cross section, so the cable is shaped like a cylinder. The length of the cable is the height of the cylinder.
volume of cylinder = (pi)(r^2)h
where r = radius of cylinder, and h = height of cylinder.
First, we convert the radius into meters.
r = 0.85 cm = 0.85 cm * (1 m)/(100 cm) = 0.0085 m
Now we find an expression for the volume of the cable in cubic meters in terms of h, the unknown height which is the length of the cable.
volume = (pi)(0.0085 m)^2 * h
volume = 0.00022698 m^2 * h <------ first expression for volume
Now we use the density and given mass to find the volume of the cable.
density = mass/volume
volume = mass/density
volume = (2450 kg)/(7950 kg/m^3) <------ second expression for volume
Set the two expressions for volume equal and solve for h.
0.00022698 m^2 * h = (2450 kg)/(7950 kg/m^3)
h = [(2450 kg)/(7950 kg/m^3)]/(0.00022698 m^2)
h = 1357.7 m
