A solid rectangular block of dimension 4.4 m, 2.6 m, 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
Given: length of the block = l = 4.4 m
Width of the block = w = 2.6 m
Height of the block = h = 1 m
Inner radius of pipe = r = 30 cm = 0.3 m
Thickness of pipe = t = 5 cm = 0.05 m
∴ outer radius of pipe as seen in the cross section of pipe = R = r + t = 30 + 5 = 35 cm = 0.35 m
Let l be the length of the pipe
Formula: volume of block = l × w × h
= 4.4 × 2.6 × 1
= 11.44 m3
Volume of block = 11.44 m3
Volume of pipe = π × (radius)2 × (length)
Volume of pipe material = volume of full pipe(R = 0.35) – volume of hollow cylinder(r = 0.3)
= π × 0.352 × l - π × 0.32 × l
= π × l × [(35/100)2 - (3/10)2]
= π × l × [(35/100) + (3/10)] × [(35/100) - (3/10)]
= (22/7) × l × (13/400) m3
∴ volume of pipe material = (22/7) × l × (13/400) m3
The pipe is made from the block
∴ volume of block = volume of pipe material
∴ 11.44 = (22/7) × l × (13/400)
∴ l = 28 × 4
∴ l = 112 m
Length of the pipe = 112 m