A solid iron cuboidal block of dimensions 4.4m × 2.6m × 1m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find length of the pipe?
The volume is the space occupied by any solid shape.
Answer: The length of the hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm is 11200cm or 112m
Let's find the length of the pipe.
Given: Dimesions of the cuboid is 4.4m × 2.6m ×1m
Length (L) = 4.4m
Breadth (B) = 2.6m
Height (H) = 1m
Let the inner radius of the hollow cylindrical pipe be 'r'
Thus, r = 30cm
Let the thickness of the hollow cylindrical pipe be 'x'
x = 5cm
Let length of the hollow cylindrical pipe be 'h'
Let the outer radius of the pipe be 'R'
Outer radius = Inner radius + thickness
Thus, R = r + x = 30 + 5 = 35cm
Since the cuboidal block is casted into a hollow cylinder, the volume will remain constant
=> L × B × H = π (R2- r2) h
=> 440 × 260 ×100 = (22/7) × (352 - 302) × h
=> h = (440 × 260 ×100 × 7) / (22 × 325) (By transposing terms)
=> h = 11200cm or 112m (since, 100cm = 1m)