Final answer:
The mass of the steel pipe is calculated by finding the volume of steel (subtracting the inner cylinder's volume from the outer cylinder's volume) and multiplying by the steel's density. The steel's volume is the difference between the volumes described by the outer and inner diameters, and the resulting mass to the nearest gram is found through this calculation.
Step-by-step explanation:
The mass of the steel pipe can be calculated by finding the volume of steel used and then multiplying it by the density. To find the volume of steel, we need to subtract the volume of the space from the volume of the outer cylinder. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. For the outer cylinder with an outside diameter of 2 cm (radius of 1 cm), the volume is V1 = π(1 cm)^2(100 cm). For the inner hollow cylinder with an inside diameter of 1.8 cm (radius of 0.9 cm), the volume is V2 = π(0.9 cm)^2(100 cm). The volume of steel is V = V1 - V2. Finally, we multiply the volume of steel by the density of steel to get the mass:
M = V * density of steel.
Inserting the values and completing the calculation:
- V1 = π(1 cm)^2(100 cm) = 100π cm^3
- V2 = π(0.9 cm)^2(100 cm) = 81π cm^3
- V = 100π cm^3 - 81π cm^3 = 19π cm^3
- Mass = 19π cm^3 * 7.8 g/cm^3
Calculating the above, we get the mass of the pipe to the nearest gram.