To calculate the average density of solid S, we need to first find the total mass of solid S and then divide it by the total volume of solid S.
Let's start by finding the volumes of the frustum, cone, and hemisphere.
Volume of cone = (1/3)πr²h = (1/3)π(3.6)²(6.4) ≈ 82.99 cm³
Volume of frustum = (1/3)πh (r₁² + r₂² + r₁r₂)
= (1/3)π(3.2)(3.6² + 3.2² + 3.2*3.6) ≈ 43.97 cm³
Volume of hemisphere = (2/3)πr³ = (2/3)π(3.6/2)³ ≈ 22.62 cm³
Total volume of solid S = volume of cone + volume of frustum + volume of hemisphere
≈ 82.99 + 43.97 + 22.62
≈ 149.58 cm³
Next, we can find the masses of the frustum and hemisphere using their densities and volumes:
Mass of frustum = density × volume = 2.4 × 43.97 ≈ 105.53 g
Mass of hemisphere = density × volume = 4.8 × 22.62 ≈ 108.50 g
To find the mass of the cone, we need to subtract the mass of the frustum from the mass of the solid cone:
Mass of cone = density × volume of cone - mass of frustum
= 2.4 × 82.99 - 105.53
≈ 100.60 g
Total mass of solid S = mass of cone + mass of frustum + mass of hemisphere
≈ 100.60 + 105.53 + 108.50
≈ 314.63 g
Finally, we can calculate the average density of solid S by dividing the total mass by the total volume:
Average density of solid S = total mass / total volume
≈ 314.63 / 149.58
≈ 2.104 g/cm³
Therefore, the average density of solid S is approximately 2.104 g/cm³.