Mass Calculation of a Spherical Shell?

📌 CONCEPT: The problem requires us to calculate the mass of a spherical shell using its volume and density, given that it requires a certain amount of paint to cover its surface.

📐 RULE / FORMULA: The surface area of a spherical shell is given by A = 4 π (R^2 - r^2), and the volume is given by V = (4/3) π (R^3 - r^3), where R is the outer radius and r is the inner radius. The density (μ) is related to mass (m) and volume (V) by the formula μ = m/V.

💡 WORKED EXAMPLE: Given a spherical shell with inner radius (r) = 12 cm and outer radius (R) = 18 cm, and a density (μ) of 0.6 g/cm³, we can calculate its volume (V) using the formula V = (4/3) π (R^3 - r^3) and then use the density formula to find the mass (m). Using the surface area formula, we can also find the mass if the paint required is given. For instance, if the paint covers an area of 4 π (R^2 - r^2), then the total mass of the shell can be calculated using the given paint mass.

⚠️ COMMON MISTAKE: Students often forget to use the correct formula for the volume and surface area of a spherical shell, or they incorrectly calculate the paint-covered area.