A hollow cylindrical iron pipe is of length 35 cm . It's outer and inner diameters are 10cm and 8cm respectively . Find the weight of the pipe if 1 cube centimeter of iron weights 7 gram
6.93 kg
the volume of the metal is
π(5^2 - 4^2)(35) cm^3
Now you can find the weight.
To find the weight of the pipe, we first need to find its volume. Since it is a hollow cylinder, we can find the volume by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
Volume of outer cylinder = π * (radius_outer)^2 * height
Volume of inner cylinder = π * (radius_inner)^2 * height
Given:
Outer diameter = 10 cm
Inner diameter = 8 cm
Length = 35 cm
Let's find the radius of both the inner and outer cylinders:
Radius_outer = outer diameter / 2 = 10 cm / 2 = 5 cm
Radius_inner = inner diameter / 2 = 8 cm / 2 = 4 cm
Substituting the values:
Volume of outer cylinder = π * (5 cm)^2 * 35 cm
Volume of inner cylinder = π * (4 cm)^2 * 35 cm
Now, let's calculate the volumes:
Volume of outer cylinder = π * 25 cm^2 * 35 cm
Volume of inner cylinder = π * 16 cm^2 * 35 cm
Next, subtract the volume of the inner cylinder from the volume of the outer cylinder to get the volume of the hollow pipe:
Volume of hollow pipe = Volume of outer cylinder - Volume of inner cylinder
Finally, multiply the volume of the hollow pipe by the weight of 1 cm^3 of iron to obtain the weight of the pipe:
Weight = Volume of hollow pipe * 7 grams/cm^3
You can substitute the values and calculate the weight of the pipe.
To find the weight of the cylindrical iron pipe, we need to calculate its volume first.
1. Calculate the volume of the outer cylinder:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
The outer radius (R) of the cylinder is half of its outer diameter, so R = 10 cm / 2 = 5 cm.
The height (h) of the cylinder is given as 35 cm.
So, the volume (V1) of the outer cylinder is:
V1 = πR^2h = π(5 cm)^2 × 35 cm = 875π cm^3.
2. Calculate the volume of the inner cylinder:
Similarly, calculate the volume (V2) of the inner cylinder using the inner radius (r = 8 cm / 2 = 4 cm) and the same height (h = 35 cm):
V2 = πr^2h = π(4 cm)^2 × 35 cm = 560π cm^3.
3. Calculate the volume of the hollow pipe:
The volume of the pipe is the difference between the volume of the outer cylinder and the inner cylinder:
V = V1 - V2 = 875π cm^3 - 560π cm^3 = 315π cm^3.
4. Calculate the weight of the pipe:
Given that 1 cm^3 of iron weighs 7 grams, we can multiply the volume of the pipe (in cm^3) by the weight of 1 cm^3 of iron (7 grams) to get the weight of the pipe (in grams):
Weight = V × 7 = 315π cm^3 × 7 grams/cm^3.
To get the numerical approximation, we can multiply the value of π by 3.14:
Weight ≈ 315 × 3.14 × 7 grams = 69258.6 grams ≈ 69.26 kg (rounded to two decimal places).
Therefore, the weight of the hollow cylindrical iron pipe is approximately 69.26 kg.