Explanation:
The total surface area is:
A = 2πr² + 2πrL
A = 2π (3.3 cm)² + 2π (3.3 cm) (12 cm)
A = 317.24 cm²
If ρ is the mass per area density in g/cm², then:
m = ρA
50 g = ρ (317.24 cm²)
ρ = 0.158 g/cm²
(a) The mass of the lid is:
m = ρA = ρ πr²
m = (0.158 g/cm²) (π (3.3 cm)²)
m = 5.39 g
(b) The mass of the shell is:
M = ρA = ρ 2πrL
M = (0.158 g/cm²) (2π (3.3 cm) (12 cm))
M = 39.22 g
(c) The moment of inertia of the lid/bottom is I = 1/2 mr².
The moment of inertia of the shell is I = Mr².
The total moment of inertia is:
I = 1/2 mr² + Mr² + 1/2 mr²
I = (m + M) r²
I = (5.39 g + 39.22 g) (3.3 cm)²
I = 485.78 g cm²
