A piece of gold wire has a diameter of 0.175 cm. How much will precisely 1.00 x 10^5 of the wire weight?

To determine the weight of the gold wire, we need to calculate its volume and then use the density of gold to find the mass. To do this, we'll assume the wire is cylindrical and use the formula for the volume of a cylinder, which is V = πr²h, where r is the radius of the cylinder and h is the height (or length in the case of wire).

Step 1: Convert the diameter to the radius by dividing by 2. Radius (r) = Diameter / 2 = 0.175 cm / 2 = 0.0875 cm

Step 2: Since we're looking for the weight of exactly 1.00 x 10^5 cm of wire, that is our height (h). Height (h) = 1.00 x 10^5 cm

Step 3: Calculate the volume of the wire using the volume formula for a cylinder. V = πr²h = π * (0.0875 cm)² * (1.00 x 10^5 cm)

Step 4: Carry out the calculations. V ≈ 3.1416 * 0.00765625 cm² * 1.00 x 10^5 cm V ≈ 2405.2785 cm³

Step 5: Look up the density of gold. Gold has a density of approximately 19.32 grams per cubic centimeter.

Step 6: Calculate the mass using the density formula which is mass (m) = density (ρ) * volume (V). m = ρ * V = 19.32 g/cm³ * 2405.2785 cm³

Step 7: Perform the final calculation to find the mass. m ≈ 46465.78052 g

Step 8: Convert the mass into kilograms (if necessary) since 1 kg = 1000 g. m ≈ 46.46578052 kg

So, 1.00 x 10^5 cm of gold wire will weigh approximately 46.466 kg.