The answer is: 6912 cubic centimeters.
We have been told the figure is a pipe.
The pipe is like a cylinder. However, this pipe, we are told, is hollow. How do we know this? Because we are told it has an inner radius of 5cm and an outer radius of 6cm.
For a better visualization of the question, see a sketch of the pipe below:
The diagram above gives the pictorial description of the question
We are told to find the volume of the metal contained in the pipe. This means that we want to know the amount of metal material was used to make this hollow pipe.
To do this, we must calculate the volume of the bigger cylinder i.e. the one with 6cm as the radius, and subtract the volume of the smaller cylinder with a radius, 5cm
The Volume of a cylinder is given as:
where r is the radius of the cylinder and h is the height or length of the cylinder.
This volume gives the amount of material that would have been contained in a cylinder of radius r and height or length h.
From this formula, we can calculate the volumes of both the larger cylinder and the smaller cylinder. That is, we can know the amount of material contained in the big and small cylinders individually.
However, because the pipe is hollow, we must subtract the volume of the smaller cylinder from that of the larger cylinder in order to get the amount of material used for making the pipe.
The formula for this is given below:
Where h is the length of the pipe = 2m = 2 x 100 cm = 200cm
R is the radius of the bigger cylinder = 6cm
r is the radius of the smaller cylinder = 5cm
Thus, with the formula in place and all the values known, we can proceed to calculate the volume of metal contained in the pipe.
![\begin{gathered} \text{Volume of Pipe =}\pi*200*(6^2-5^2) \\ \text{Volume of Pipe=}\pi*200(36-25)=\pi*200*11 \\ \\ \text{Volume of Pipe = 2200}\pi cm^3 \\ \\ \therefore volumeofPipe=6911.50cm^3\approx6912\operatorname{cm}^3\text{ (to nearest cubic centimeter} \end{gathered}]()
Therefore the final answer is: 6912 cubic centimeters.