To determine how a solid iron cuboidal block can be cast into a hollow cylindrical pipe, we first need to calculate the volume of the cuboidal block and then find the volume of the hollow cylindrical pipe.
Step 1: Calculate the volume of the cuboidal block.
Given the dimensions of the block are:
- Length (l) = 44 m
- Width (w) = 26 m
- Height (h) = 1 m
The volume (V) of the cuboidal block can be calculated using the formula:
V = l × w × h
Substituting the values:
V = 44 m × 26 m × 1 m = 1144 m³
Step 2: Calculate the volume of the hollow cylindrical pipe.
To find the volume of the hollow cylindrical pipe, we need to calculate the volume of the outer cylinder and subtract the volume of the inner cylinder.
Given:
- Internal radius (r) = 30 cm = 0.3 m
- Thickness = 5 cm = 0.05 m
- So, the external radius (R) = internal radius + thickness = 0.3 m + 0.05 m = 0.35 m
Let’s assume the height (H) of the pipe is equal to the height of the cuboidal block, which is 1 m.
Volume of the outer cylinder (V_outer):
V_outer = πR²H = π(0.35 m)²(1 m) = π(0.1225 m²)(1 m) ≈ 0.3847 m³
Volume of the inner cylinder (V_inner):
V_inner = πr²H = π(0.3 m)²(1 m) = π(0.09 m²)(1 m) ≈ 0.2827 m³
The volume of the hollow cylindrical pipe (V_pipe):
V_pipe = V_outer – V_inner ≈ 0.3847 m³ – 0.2827 m³ ≈ 0.102 m³
Conclusion:
The volume of the solid iron cuboidal block (1144 m³) is much greater than the volume of the hollow cylindrical pipe (0.102 m³). Thus, the solid iron block cannot be cast into the hollow cylindrical pipe as its volume exceeds that of the pipe.