Find the mass of a cylindrical iron pipe 2.1m long and 12cm in external diameter, if the metal is 1cm thick and of density 7.8g/cm cube. Take π=22/7
How did u get 210cm^3
Where is my answer
impatient much?
the volume of a cylinder is base area * length
you have a circular base, but with a hole in it. Such a ring of inner radius r and outer radius R has area
a = π(R^2-r^2)
So, your pipe has an outer radius R=6cm and an inner radius r=5cm
That makes the volume of metal
π(6^2-5^2) * 210 cm^3
and, as you know, mass = density * volume
= 7.8 * π(6^2-5^2) * 210 = _______ grams
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!
To find the mass of the cylindrical iron pipe, we can use the formula:
Volume = π * (r^2 - (r - t)^2) * h,
where:
- π is a mathematical constant and is approximately equal to 22/7,
- r is the external radius of the pipe,
- t is the thickness of the metal,
- h is the height or length of the pipe.
First, let's convert the given measurements to be consistent. The external diameter is given as 12 cm, so the external radius (r) is half of that, which is 12 cm / 2 = 6 cm.
Next, we need to convert the thickness (t) from 1 cm to meters to maintain consistency with the length measurement. 1 cm is equal to 0.01 m.
Now, we can substitute the values into the formula to calculate the volume of the metal:
Volume = (22/7) * (6^2 - (6 - 0.01)^2) * 2.1,
Calculating this equation will give us the volume of the metal in cubic meters.
Finally, to find the mass, we use the formula:
Mass = Volume * Density,
where the density is given as 7.8 g/cm^3. However, since we converted the volume to cubic meters, we need to convert the density from g/cm^3 to kg/m^3. 1 g/cm^3 is equal to 1000 kg/m^3.
Once we have the mass value, we can provide the final answer.