Final answer:
The length of the cylindrical bar is approximately 27.54 cm.
Step-by-step explanation:
To find the length of the cylindrical bar, we need to first calculate the volume of the metal disc and then use that volume to calculate the length of the bar.
The volume of the metal disc can be calculated using the formula for the volume of a cylinder: V = πr^2h. The diameter of the metal disc is 12cm, so the radius is half of that, which is 6cm. The height of the disc is 5cm, so the volume of the disc is:
V = π(6cm)^2(5cm) = 540π cm^3.
Next, we can calculate the length of the cylindrical bar. The diameter of the bar is 5cm, so the radius is half of that, which is 2.5cm. We can use the formula for the volume of a cylinder again, this time rearranging it to solve for the height:
V = πr^2h => h = V/(πr^2) = (540π cm^3)/(π(2.5cm)^2) = (540π cm^3)/(19.63 cm^2) ≈ 27.54 cm.
Therefore, the length of the cylindrical bar is approximately 27.54 cm.