find the mass of a cylindrical iron pipe 2.1m long and 12cm in external diameter,of the metal is 1 cm thick and of density 7.8g/cm3 (take π=22/7)
volume = π r^2 h
volume of "solid" = π(6^2)(210) = 7560π cm^3
volume of part to be taken out = π(5^2)(210) = 5250π cm^3
volume of your pipe = 7560π cm^3 - 5250π cm^3
= 2310π cm^3
mass = 2310π(7.8) g = appr 56605.2 g or appr 56.6 kg
I used the actual value of π
on my calculator, why use 22/7 for π in 2021 ?
If you insist on using 22/7 redo the calculations
Well, let's calculate it with a touch of humor, shall we? Time to get into the "iron" mood!
First, we need to find the volume of the cylinder. Since it's "iron"-ic, we'll have to determine the volume of the outer cylinder and the inner cylinder. Ready?
The outer cylinder's radius will be half of the external diameter, which is 12 cm. Now, let me pop out my "iron"-ing board for calculations. So, the outer cylinder has a radius of 6 cm and a height of 210 cm.
Using the formula for the volume of a cylinder (π * r² * h), we can determine the volume of the outer cylinder. But remember, we'll have to subtract the volume of the inner cylinder later, because it's a "ma-steel-ious" layer!
Now, let's talk "man-tenance" for a moment. The inner cylinder, being the metal layer, will have a radius of 6 cm minus 1 cm, as the thickness of the metal is 1 cm.
Using the same formula, the volume of the inner cylinder will be calculated by taking the difference in radii. Is everybody following? Stay "focused" now!
Once we have both volumes, subtract the inner cylinder's volume from the outer cylinder's volume to find the volume of the "tub-ular" iron pipe.
Now, the final stretch! Multiply the volume of the iron pipe by the density of iron, which is given as 7.8 g/cm³. Drumroll, please...
*Bum-bada-dum-bum-dum-bum!*
The resulting mass of the cylindrical iron pipe will be your "iron-ly" answer!
To find the mass of the cylindrical iron pipe, we need to calculate the volume and then multiply it by the density.
1. Calculate the external radius (r):
The external diameter is given as 12 cm. The radius (r) is half of the diameter, so:
r = 12 cm / 2 = 6 cm
2. Calculate the internal radius (r_inner):
The thickness of the metal is given as 1 cm.
r_inner = r - thickness = 6 cm - 1 cm = 5 cm
3. Calculate the height (h):
The length of the pipe is given as 2.1 m. However, we need to convert it to cm:
h = 2.1 m × 100 cm/m = 210 cm
4. Calculate the volume (V) of the cylindrical pipe:
The formula for the volume of a cylinder is V = π * (r^2 - r_inner^2) * h.
Using the value of π as 22/7, the calculation becomes:
V = (22/7) * (6^2 - 5^2) * 210 cm^3
5. Calculate the mass (m):
The formula for mass (m) is m = density * volume.
The density is given as 7.8 g/cm^3.
m = density * V = 7.8 g/cm^3 * V
Now, let's calculate the values:
Step 1: r = 6 cm
Step 2: r_inner = 5 cm
Step 3: h = 210 cm
Step 4: V = (22/7) * (6^2 - 5^2) * 210 cm^3
Step 5: m = 7.8 g/cm^3 * V
Performing the calculations:
Step 4: V = (22/7) * (36 - 25) * 210 cm^3
V = (22/7) * 11 * 210 cm^3
V = 6930 cm^3
Step 5: m = 7.8 g/cm^3 * 6930 cm^3
m = 54054 g
Therefore, the mass of the cylindrical iron pipe is 54054 grams or 54.054 kilograms.
To find the mass of the cylindrical iron pipe, we need to calculate the volume of the pipe and then multiply it by the density of the iron.
Step 1: Calculate the external and internal radii of the pipe.
The external diameter of the pipe is given as 12 cm. To find the external radius, divide the diameter by 2:
External Radius (r₁) = External Diameter / 2 = 12 cm / 2 = 6 cm.
The thickness of the metal is given as 1 cm, so the internal radius can be found by subtracting the thickness from the external radius:
Internal Radius (r₂) = External Radius - Thickness = 6 cm - 1 cm = 5 cm.
Step 2: Calculate the volume of the pipe.
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Since the pipe is 2.1 m long, we need to convert it to centimeters:
Height (h) = 2.1 m x 100 cm/m = 210 cm.
Now, we can calculate the volume of the pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:
V = πr₁²h - πr₂²h.
Step 3: Calculate the mass of the pipe.
The density of the iron is given as 7.8 g/cm³. We can use the equation M = ρV, where M is the mass, ρ is the density, and V is the volume, to calculate the mass of the pipe.
Mass (M) = Density (ρ) x Volume (V).
Substitute the values into the equation and solve for the mass.
Finally, convert the mass from grams to kilograms by dividing by 1000 if needed.
Let's perform the calculations:
External Radius (r₁) = 6 cm
Internal Radius (r₂) = 5 cm
Height (h) = 210 cm
Volume (V) = πr₁²h - πr₂²h
Volume (V) = π(6 cm)²(210 cm) - π(5 cm)²(210 cm)
Volume (V) = (22/7) x 6² x 210 - (22/7) x 5² x 210 (using π = 22/7)
Volume (V) = 27720 cm³
Density (ρ) = 7.8 g/cm³
Mass (M) = ρV
Mass (M) = 7.8 g/cm³ x 27720 cm³
Mass (M) = 216216 g (grams)
The mass of the cylindrical iron pipe is 216216 g or 216.216 kg.