Calculating the Volume of the Iron Block
The first step in solving the problem is to determine the volume of the solid iron cuboidal block. The volume (V) of a cuboid is calculated using the formula:
V = Length × Width × Height
Given the dimensions of the block:
- Length = 44 m
- Width = 26 m
- Height = 1 m
Let’s calculate the volume:
V = 44 m × 26 m × 1 m = 1144 m³
Calculating the Volume of the Hollow Cylinder
Next, we need to determine the volume of the hollow cylindrical pipe into which the block is being cast. The volume of a hollow cylinder can be calculated using the formula:
Volume = πh(R² – r²)
where:
- h = height (length) of the cylinder
- R = outer radius
- r = inner radius
Given parameters:
- Internal radius (r) = 30 cm = 0.3 m
- Thickness = 5 cm = 0.05 m
- Outer radius (R) = Internal radius + Thickness = 0.3 m + 0.05 m = 0.35 m
- Height (h) = To be determined; let’s assume it is equal to the height of the cuboid (1 m) for now.
Substituting the values into the volume formula:
Volume = π × 1 m × (0.35 m² – 0.3 m²)
= π × 1 m × (0.1225 m² – 0.09 m²)
= π × 1 m × (0.0325 m²)
= π × 0.0325 m³ ≈ 0.102 m³ (using π ≈ 3.14)
Determining Feasibility
Now that we have the volumes, we can determine if the solid cuboidal block can be cast into the hollow cylindrical pipe:
- Volume of iron block = 1144 m³
- Volume of hollow cylinder ≈ 0.102 m³
Clearly, the volume of the hollow cylindrical pipe is much smaller than that of the solid cuboidal block, indicating that the block cannot be cast into the hollow cylindrical pipe as it exceeds the available volume.