Sure, let's calculate the mass of the cylindrical iron pipe. Let's assume the density of the pipe doesn't change as a result of the 1cm thickness of the metal. Are you ready for some funny math?
First, let's find the volume of the overall cylinder. The external diameter is 12 cm, so the radius would be half of that, which is 6 cm ➜ *Please hold... converting to inches* ➜ 2.36 inches rounded up. So, the radius is approximately 2.36 inches.
Now, the length of the pipe is given as 2.1 meters, which is roughly 82.68 inches. So, using the formula for the volume of a cylinder, we'll multiply the square of the radius by the length and the value of pi, which is roughly 3.14. But hold your horses! We were given a different value for pi. Okay, let's work with π=22/7 to avoid any shopping cart scandals.
The volume of the external cylinder = (22/7) * (2.36)² * 82.68 cubic inches. Are you still following me, or do you need a unicycle to get your bearings?
Now, to determine the volume of the internal cylinder (the hollow part), we need to subtract the volume of the metal (which is the thickness of the pipe) from the external volume.
The internal diameter is obtained by subtracting twice the thickness from the external diameter. Since the external diameter is 12 cm, and the thickness is 1 cm, we have an internal diameter of 12 - 2(1) cm, which is a diameter of 10 cm.
Converting this to inches, we get approximately 3.94 inches. Thus, the internal radius is about 1.97 inches to be more precise.
Now, we can calculate the volume of the internal cylinder using the same formula as before ➜ (22/7) * (1.97)² * 82.68 cubic inches.
So, to find the volume of the iron itself, we subtract the volume of the internal cylinder from the volume of the external cylinder.
Finally, to find the mass, we need to multiply the volume by the density of the iron, which is given as 7.8 g/cm³. But remember, we have the answer in cubic inches, so we'll need some additional conversion voodoo.
Once we manage all that, we'll have the mass of the cylindrical iron pipe. But I'd have to use a calculator the size of a circus tent to simplify all these calculations!