A solid iron cuboidal block of dimensions is cast into a hollow cylindrical pipe of internal radius and thickness . Find length of the pipe.
Step 1: Find the volume of cylindrical pipe
Dimensions of cuboidal block
Dimensions of cylindrical pipe:
So the outer radius
Let the length of the pipe
We know, the volume of a hollow cylinder ,
We know, when a shape is recast into a different shape, then the volume stays the same.
Here, Cuboidal block is recast into cylindrical pipe. So, volume of the cuboidal block equals the volume of hollow cylinder.
We know, Volume of a cuboidal tank
Then, Volume of cylindrical pipe will also be [ Because the cuboidal tank is melt and recast into the cylindrical pipe]
Step 2: Find the height of the pipe
Also, we have volume of a hollow cylinder
So equating the above two, we get:
Now, putting the values of in the equation above, we get:
Thus, the length of the pipe is