A roll of aluminum wire is used to make finishing nails (nails that do not have heads). If the nails are 5.00cm long and 0.300cm in diameter and the roll of wire has a mass of 225kg, how many nails can be made from one roll?

We need to determine the volume of one nail and then calculate how many nails can be made from the total volume of the roll of wire. The volume of one nail can be found using the formula for the volume of a cylinder: V = ?r^2h where r is the radius (half the diameter) and h is the height (or length) of the nail. r = 0.300cm / 2 = 0.150cm h = 5.00cm V = ?(0.150cm)^2(5.00cm) V = 0.3534 cm^3 To find out how many nails can be made from the roll of wire, we need to determine the total volume of the wire. We know its mass (225kg) and its density (2.70 g/cm^3 for aluminum). Density = mass / volume volume = mass / density = (225 kg) / (2.70 g/cm^3 x 1000 g/kg) = 83,333.33 cm^3 Dividing the total volume of the wire by the volume of one nail gives: Number of nails = 83,333.33 cm^3 / 0.3534 cm^3 per nail ? 235,483 nails Therefore, \approx imately 235,483 nails can be made from one roll of aluminum wire.