Question

a bead is made from material with constant density 5 grams per cubic millimeter by drilling a cylindrical hole of radius 1 mm through a sphere of radius 6 mm. (a) set up a triple integral in cylindrical coordinates representing the mass of the bead in grams (do not include units). if necessary, enter as theta. a

Answer 1

The density of the jewelry is calculated by dividing its mass by the volume of water it displaces. By comparing this density with those of known materials, the substance the jewelry is likely made of can be inferred.

Step-by-step explanation:

To calculate the density of the jewelry piece, you would use the formula density = mass / volume. The volume of the jewelry can be determined by the water displacement method: the increase in the water level once the jewelry is submerged. Given the mass of the jewelry (132.6 g) and the volume displacement (from 48.6 mL to 61.2 mL), the density of the jewelry is calculated as follows:

• Volume displaced = Final Volume - Initial Volume = 61.2 mL - 48.6 mL = 12.6 mL
• Density = Mass of Jewelry / Volume Displaced = 132.6 g / 12.6 mL

To identify the likely substance the jewelry is made of, you compare the calculated density with known densities of various substances. If the calculated density closely matches that of a known substance, you can infer that the jewelry is likely made of that substance.