Final answer:
The diameter of the handle of the faucet is twice its radius, which is calculated by utilizing the ideal mechanical advantage of the machine. Since the rod has a diameter of 1 cm and the IMA is 6, the radius is 6 cm, thus the diameter of the handle is 12 cm.
Step-by-step explanation:
The question refers to the ideal mechanical advantage (IMA) of a machine, which is the ratio of the diameter of the handle to the diameter of the shaft of the faucet. Given that the handle of the faucet is 10 cm long and the diameter of the shaft of the faucet is asked to be compared with this length, the length of the handle can be seen as essentially representing the lever arm of the machine. The IMA is 6, indicating that the length of the handle is six times the diameter of the rod attached to the handle that controls the valve. Since the rod has a diameter of 1 cm, 6 times this diameter (6 x 1 cm) gives us the radius of the handle, which is 6 cm (Answer D from the provided reference). However, as we need the diameter, we multiply the radius by two, giving us a diameter of 12 cm for the handle.