calculate the mass of a 4.50 m long copper rod that has the diameter of 1.25cm. the density of copper is 8.94 g/ml
To calculate the mass of the copper rod, we can use the formula:
Mass = Volume x Density
To find the volume of the copper rod, we need to first calculate its cross-sectional area using the diameter provided.
The diameter is given as 1.25 cm. To find the radius, we need to divide the diameter by 2:
Radius = Diameter / 2
Radius = 1.25 cm / 2
Radius = 0.625 cm
Next, we need to convert the radius from centimeters to meters by dividing by 100:
Radius = 0.625 cm / 100
Radius = 0.00625 m
Now that we have the radius, we can calculate the cross-sectional area using the formula:
Area = π x radius^2
Area = π x (0.00625 m)^2
Area = 0.0000309 m^2
Next, we can calculate the volume of the copper rod by multiplying the cross-sectional area by its length:
Volume = Area x Length
Volume = 0.0000309 m^2 x 4.50 m
Volume = 0.00013905 m^3
Finally, we can calculate the mass of the copper rod using the volume and density:
Mass = Volume x Density
Mass = 0.00013905 m^3 x 8.94 g/ml
Since the density of copper is given in g/ml, we need to convert the volume from m^3 to ml. Since 1 m^3 is equal to 1,000,000 ml, we can multiply the volume by 1,000,000:
Mass = (0.00013905 m^3 x 1,000,000 ml/m^3) x 8.94 g/ml
Mass = 139.05 ml x 8.94 g/ml
Mass = 1241.457 g
Therefore, the mass of the copper rod is approximately 1241.457 grams.