Final answer:
The length of the wire with a volume of 66 cubic centimetres and a diameter of 1 mm, you would use the volume formula for a cylinder and rearrange it to solve for the height (length of the wire), convert the units to meters, and then perform the calculation.
Step-by-step explanation:
The question is asking to find the length of a wire made of silver with a volume of 66 cubic centimetres and a diameter of 1 mm.
To solve this problem, we need to use the formula for the volume of a cylinder (V = πr^2h), where V is the volume, r is the radius, and h is the height, or in this case, the length of the wire.
Since the diameter is 1 mm, the radius r is 0.5 mm, or 0.0005 meters. We can rearrange the formula to solve for h (the length) and substitute the given values:
V = πr^2h
→ h = V / (πr^2)
Substituting the values:
h = 66 cm^3 / (π * (0.0005 m)^2)
→ h = 66 * 10^-6 m^3 / (3.14159 * (0.0005 m)^2)
→ h = 66 * 10^-6 m^3 / (7.853975 * 10^-7 m^2)
After calculating h, we would convert the result into meters to find the length of the wire in meters.