Q. 184.9( 8 Votes )

# 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.

Answer :

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 m^{3}

Volume of block = 11.44 m^{3}

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 × 0.35^{2} × l - π × 0.3^{2} × l

= π × l × [(35/100)^{2} - (3/10)^{2}]

= π × l × [(35/100) + (3/10)] × [(35/100) - (3/10)]

= (22/7) × l × (13/400) m^{3}

∴ volume of pipe material = (22/7) × l × (13/400) m^{3}

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

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