Question

A solid 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.

Answer 1

We have, 

Length of the rectangular block l = 4.4 m,

Breadth of the rectangular block, b = 2.6 m,

Height of the rectangular block, h = 1 m,

Internal radius of the cylindrical pipe, r = 30 cm = 0.3 m and 

Thickness of the pipe = 5 cm = 0.05 m

Also, the external radius of the pipe = 0.3 + 0.05 = 0.35 m

Let the length of the pipe be H.

Now, 

Volume of the pipe = volume of the block

⇒ πR²H - πr²H = lbh

⇒ π(R² - r²) H = lbh

`=> 22/7xx(0.35^2 - 0.3^2)"H" = 4.4 ×2.6×1`

`=>22/7xx(0.1225 - 0.09)"H" =4.4xx2.6`

`=>22/7xx0.0325xx"H" = 4.4xx2.6`

`=> "H" = (4.4xx2.6xx7)/(22xx0.0325)`

∴ H = 112 m

So, the length of the pipe is 112 m.