Final answer:
The mass of the lead cylinder can be determined by calculating its volume using the formula for the volume of a cylinder, converting that volume from cubic inches to milliliters, and then multiplying by the density of lead (11.4 g/ml) to find the mass in grams.
Step-by-step explanation:
The question asks for the mass of a cylinder of lead with a given diameter and length, using the density of lead to calculate it. First, we need to find the volume of the cylinder, which can be calculated using the formula for the volume of a cylinder, ℝV = πr²h, where π is Pi (approximately 3.14159), r is the radius, and h is the height. The diameter is given as 1.80 inches, so the radius is half of that, 0.90 inches. The length of the cylinder, which is the same as the height in the volume formula, is 4.12 inches. Since the density is given in grams per milliliter (g/ml), we need to convert the volume from cubic inches to milliliters before we can calculate the mass.
To convert cubic inches to milliliters, we use the conversion factor 1 cubic inch = 16.387064 milliliters. After obtaining the volume in milliliters, we can multiply it by the density of lead (11.4 g/ml) to find the mass in grams.