The Kohinoor Diamond \(\left(d=3.51 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is 108 carats. If one carat has a mass of \(2.00 \times 10^{2} \mathrm{mg}\), what is the mass of the Kohinoor Diamond in pounds? What is the volume of the diamond in cubic inches?

Answer: To find the mass in pounds and the volume in cubic inches of the Kohinoor Diamond, follow these steps: 1. Convert the mass of the diamond from carats to grams using the conversion factor 1 carat = 2.00 × 10² mg and then to grams: mass in grams = mass in carats × (2.00 × 10² mg / 1 carat) × (1 g / 1000 mg). 2. Calculate the mass of the diamond in pounds using the conversion factor 1 pound = 453.59237 grams: mass in pounds = mass in grams × (1 pound / 453.59237 grams). 3. Calculate the volume of the diamond in cubic centimeters using the mass in grams and the density formula: volume in cubic centimeters = mass in grams / density in g / cm³. 4. Convert the volume of the diamond to cubic inches using the conversion factor 1 cubic inch = 16.3871 cubic centimeters: volume in cubic inches = volume in cubic centimeters × (1 cubic inch / 16.3871 cm³).