A uniform cylindrical pipe has an external diameter of 3.6cm and an internal diameter of 2.8cm.
a)Calculate the volume of the material required to construct a metre length of the pipe.
b)One cubic metre of material used has a mass of 44kg.Calculate the mass of 60m of such a pipe giving your answer to the nearest kilogram.
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atomic no
volumemetal=outsidediaVolume-insidediaVol
= PI/4 * (3.6^2 -2.8^2) per meter in cm^3/m
mass60m=volume*density=volumeabove*.044kg/cm^3
To calculate the volume of the material required to construct a meter length of the pipe, we need to find the difference between the volume of the outer cylinder and the volume of the inner cylinder. The formula for the volume of a cylinder is given by:
V = π * r^2 * h
where V is the volume, r is the radius, and h is the height.
a) Volume of the outer cylinder:
For the outer cylinder, the radius (R) is half of the external diameter (D), which is 3.6 cm:
R = D / 2 = 3.6 cm / 2 = 1.8 cm = 0.018 m
The height (h) of the cylinder is given as 1 meter.
Now, we can calculate the volume (V_outer) of the outer cylinder:
V_outer = π * R^2 * h = π * (0.018 m)^2 * 1 m = 0.00102 m^3
Volume of the inner cylinder:
Similarly, for the inner cylinder, the radius (r_inner) is half of the internal diameter (d_inner), which is 2.8 cm:
r_inner = d_inner / 2 = 2.8 cm / 2 = 1.4 cm = 0.014 m
Again, the height (h) of the cylinder is 1 meter.
Now we can calculate the volume (V_inner) of the inner cylinder:
V_inner = π * r_inner^2 * h = π * (0.014 m)^2 * 1 m = 0.000616 m^3
Finally, the volume of the material required to construct a meter length of the pipe is the difference between the volumes of the outer and inner cylinders:
Volume of material = V_outer - V_inner = 0.00102 m^3 - 0.000616 m^3 = 0.000404 m^3
b) To calculate the mass of 60 meters of such a pipe, we need to multiply the volume of material required for one meter length (calculated in part a) by the length of the pipe.
Mass = Volume of material * density
Given that one cubic meter of material has a mass of 44 kg, we can calculate the mass of the pipe as follows:
Mass = Volume of material * density = 0.000404 m^3 * 44 kg/m^3 = 0.017736 kg
Therefore, the mass of 60 meters of such a pipe is:
Mass = 0.017736 kg/m * 60 m = 1.06416 kg
Rounded to the nearest kilogram, the mass of 60 meters of the pipe is approximately 1 kg.