A solid iron rectangular block of dimensions 4.4 m , 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm.Find the length of the pipe.

Explanation

Given that, a solid iron cuboid block is recast into a hollow cylindrical pipe. Length of cuboidal pipe (l ) = 4.4 m
Breadth of cuboidal pipe (b)= 2.6 m and height of cuboidal pipe (h) = 1 m
So, Volume of a solid iron cuboical block = l.b.h
`= 4.4 xx 2.6 xx 1 = 11.44 m^(3)`
Also, internal radius of hollow cylindrical pipe `(r_(1))` = 30 cm = 0.3 cm
and thickness hollow cylindrical pipe = 5 cm = 0.05 m
So, external radius of hollow cylindrical pipe `(r_(e)) = r_(i)` + Thickness
`= 0.3 + 0.05`
` = 0.35 m`
`therefore ` Volume of hollow cylindrical = Volume of cylindrical pipe = Volume of cylindrical pipe with external radius - Volume of cylindrical pipe with internal radius
`" " = pir_(e)^(2)h_(1) - pir_(i)^(2)h_(1) = pi(r_(e)^(2) - r_(i)^(2) )h_(1)`
`" "= (22)/(7) [(0.35)^(2) - (0.3)^(2)].h_(1)`
`" "= (22)/(7) xx 0.65 xx 0.05 xx h_(1) = 0.715 xx h_(1) = 0.715 xx h_(1)//7`
where, `h_(1)` be lenght of the hollow cylindrical pipe.