A solid iron rectangular block of dimensions `(2.2 m xx 1.2 m xx 1m)` is cast into a hollow cylindrical pipe of internal radius `35 cm` and thickness `5 cm.` Find the length of the pipe

Explanation

Volume of the iron block `= (220 xx 120 xx 100) cm^(3)`
Volume of iron in hollow pipe formed
`= (220 xx 120 xx 100) cm^(3)`
Internal radius of the pipe, r = 35 cm
External radius of the pipe, `R = (35 + 5) cm = 40cm`
Let the length of the pipe be x cm
Volume of iron in hollow pipe `= (pi R^(2) h - pi r^(2)h)` cu units
`= pi h (R^(2) - r^(2))`cu units
`= pi h (R + r) (R - r)` cu units
`= (22)/(7) xx x xx (40 + 35) (40 - 35) cm^(3)`
`:. (22)/(7) xx x xx 75 xx 5 = 220 xx 120 xx 100`
`rarr x = ((220 xx 120 xx 100 xx 7)/(75 xx 5 xx 22)) = 2240`
Hence, the length of the pipe is `2240 cm = 22.4 m`