A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass. (Use π = 3.14)
The mass of the pole is approximately 892.26 kg (or 892262.4 g).
Explanation
This problem involves finding the volume of a combination of two cylinders and then converting volume to mass using the given density. The pole consists of a larger cylinder at the bottom and a smaller cylinder on top. We calculate the volume of each cylinder separately using the formula V = πr²h, then add them to get the total volume. Finally, we multiply the total volume by the given mass density (8g per cm³) to find the mass.
Solution Steps
Step 1: Find the radius of the lower cylinder. Diameter = 24 cm, so Radius (r₁) = 24/2 = 12 cm
Step 2: Calculate the volume of the lower cylinder. Volume (V₁) = πr₁²h₁ = 3.14 × (12)² × 220 = × 220 = 99475.2 cm³
Step 3: Calculate the volume of the upper cylinder. Radius (r₂) = 8 cm, Height (h₂) = 60 cm Volume (V₂) = πr₂²h₂ = 3.14 × (8)² × 60 = × 60 = 12057.6 cm³
Step 4: Find the total volume of the pole. Total Volume = V₁ + V₂ = 99475.2 + 12057.6 = 111532.8 cm³
Step 5: Calculate the mass of the pole. Mass = Total Volume × 8 g/cm³ = = 892262.4 g = 892.26 kg (approximately)