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Home » A solid cuboid of iron with dimensions is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are and respectively. Find the length of pipe.
A solid cuboid of iron with dimensions 53cm\times 40cm\times 15cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8cm and 7cm respectively. Find the length of pipe.
CBSE | Class 10 | Exercise 16.1 | Maths | RD Sharma | Surface Areas And Volumes
A solid cuboid of iron with dimensions 53cm\times 40cm\times 15cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8cm and 7cm respectively. Find the length of pipe.

Assume the length of the pipe be h cm.

Formula for volume of cuboid is V=whl

Now, Volume of cuboid =\left( 53\times 40\times 15 \right)c{{m}^{3}}

Internal radius of the pipe =7/2cm=r

External radius of the pipe =8/2=4cm=R

Therefore, the volume of iron in the pipe = (External Volume) - (Internal Volume)

=\pi {{R}^{2}}h-\pi {{r}^{2}}h

=\pi h\left( {{R}^{2}}-{{r}^{2}} \right)

=\pi h\left( R-r \right)\left( R+r \right)

=\pi \left( 4-7/2 \right)\left( 4+7/2 \right)\times h

=\pi \left( 1/2 \right)\left( 15/2 \right)\times h

Now from the question it’s understood that,

The volume of iron in the pipe = volume of iron in cuboid

\pi \left( 1/2 \right)\left( 15/2 \right)\times h=53\times 40\times 15

h=\left( 53\times 40\times 15\times 7/22\times 2/15\times 2 \right)cm

h=2698cm

Hence, the length of the pipe is 2698cm.

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