Final answer:
The absorber thickness for cardboard, aluminum, and lead are 31.8 g/cm², 116.1 g/cm², and 136.8 g/cm², respectively. To find the side length of an aluminum cube with known surface density and mass, use the square root of the mass divided by the product of surface density and number of sides exposed.
Step-by-step explanation:
Calculating Absorber Thickness in g/cm²
Given the densities of cardboard, aluminum, and lead, we can calculate the absorber thickness for each material in terms of g/cm². The thicknesses in cm are 53 cm for cardboard, 43 cm for aluminum, and 12 cm for lead. Using the formula thickness (g/cm²) = density (g/cm³) × thickness (cm), the absorber thicknesses are calculated as follows:
• Cardboard: 0.6 g/cm³ × 53 cm = 31.8 g/cm²
• Aluminum: 2.7 g/cm³ × 43 cm = 116.1 g/cm²
• Lead: 11.4 g/cm³ × 12 cm = 136.8 g/cm²
Now, to compute the side length of a cube made of aluminum foil with a known surface density of 15 g/cm² and a mass of 100 g, we use the formula for volume V = side length³ and the relationship surface density = mass ÷ surface area. With these, the side length can be calculated by rearranging the formula to side length = √(mass ÷ surface density) and using the mass of 100 g.
Thus, the approximate side length would be:
side length = √(100 g ÷ 6 ÷ 15g/cm²) ≈ √(0.444 cm) ≈ 1.10 cm (Option b is correct).