A hollow iron pipe is 2.1m long and its external diameter is 4.5 cm.if the thickness of pipe is 0.25cm and weight of iron is 4 gm/cm3, then the weight of pipe is? (ans 2.805kg) ?
The outer radius R=2.25 cm
The inner radius r=2.25-0.25 = 2.0cm
So, the volume of pipe is
2.1 * π(R^2-r^2)
= 210cm * π(2.25^2-2^2)cm^2
= 701 cm^3
Now you can get the mass of the pipe.
To find the weight of the pipe, we need to calculate the volume of the iron used and then multiply it by the density of iron.
Given:
Length of the pipe (L) = 2.1 m
External diameter (D) = 4.5 cm
Thickness of the pipe (t) = 0.25 cm
Weight of iron (density) = 4 gm/cm3
First, let's convert the units to a consistent form:
Length (L): 2.1 m = 210 cm (since 1 m = 100 cm)
External diameter (D): 4.5 cm
Thickness (t): 0.25 cm
Next, we calculate the internal diameter (d) of the pipe:
Internal diameter (d) = External diameter (D) - 2 * Thickness (t)
Internal diameter (d) = 4.5 cm - 2 * 0.25 cm
Internal diameter (d) = 4.5 cm - 0.5 cm
Internal diameter (d) = 4 cm
Now, let's calculate the volume of the iron used in the pipe:
Volume of the iron used = Volume of outer cylinder - Volume of inner cylinder
Volume of outer cylinder = π * (External radius)² * Length
Volume of outer cylinder = π * (D/2)² * L
Volume of outer cylinder = π * (4.5 cm/2)² * 210 cm
Volume of inner cylinder = π * (Internal radius)² * Length
Volume of inner cylinder = π * (d/2)² * L
Volume of inner cylinder = π * (4 cm/2)² * 210 cm
Now, let's substitute the values and calculate the volumes:
Volume of outer cylinder = π * (4.5/2)² * 210 = π * (2.25)² * 210 cm³
Volume of inner cylinder = π * (4/2)² * 210 = π * (2)² * 210 cm³
Finally, let's find the volume of iron used in the pipe:
Volume of iron used = Volume of outer cylinder - Volume of inner cylinder
Volume of iron used = π * (2.25)² * 210 - π * (2)² * 210 cm³
Now, multiply the volume of iron used by the density of iron:
Weight of pipe = Volume of iron used * Weight of iron (density)
Weight of pipe = [π * (2.25)² * 210 - π * (2)² * 210] * 4 gm
Now, convert grams to kilograms:
Weight of pipe = [π * (2.25)² * 210 - π * (2)² * 210] * 4 gm / 1000 kg
Calculate the value:
Weight of pipe = [π * (2.25)² * 210 - π * (2)² * 210] * 4 / 1000 kg
Using a calculator, we get:
Weight of pipe ≈ 2.805 kg
Therefore, the weight of the pipe is approximately 2.805 kg.