To calculate the mass of the iron pipe, we need to find the volume of the pipe and then multiply it by the mass per unit volume.
Given:
Thickness of the iron = 1 cm
Mass of 1 cm³ of cast iron = 7.2 g
Length of the pipe = 2 meters
Outer radius of the pipe = 12 cm
Inner radius of the pipe = 10 cm
First, we need to find the volume of the pipe. We can calculate the difference between the volumes of the outer and inner cylinders.
Outer volume:
The outer radius of the pipe is 12 cm, so the outer volume can be calculated using the formula for the volume of a cylinder: V_outer = πr_outer²h.
V_outer = π(12 cm)²(200 cm) = 28800π cm³
Inner volume:
The inner radius of the pipe is 10 cm, so the inner volume can be calculated in the same way: V_inner = πr_inner²h.
V_inner = π(10 cm)²(200 cm) = 20000π cm³
Now, we can find the volume of the iron pipe by subtracting the inner volume from the outer volume:
V_pipe = V_outer - V_inner = 28800π cm³ - 20000π cm³ = 8800π cm³
Finally, we can calculate the mass of the pipe by multiplying the volume by the mass per unit volume:
Mass = V_pipe * (7.2 g / 1 cm³) = 8800π cm³ * 7.2 g/cm³ ≈ 19946.04 g
Therefore, the mass of a 2-meter length of the iron pipe is approximately 19946.04 grams.
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