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Answer :
Final Answer:
The weight of the pipe is equal to 3.696 kg (Option b).
Explanation:
To calculate the weight of the hollow iron pipe, we need to determine the volume of the iron used to make the pipe and then multiply it by the density of iron (8 g/cm³) to get the weight. The pipe consists of an outer cylinder and an inner cylinder, and the weight of the pipe is the difference between the weights of these two cylinders.
First, let's calculate the external and internal radii:
External radius = External diameter / 2 = 8 cm / 2 = 4 cm
Internal radius = External radius - Thickness = 4 cm - 1 cm = 3 cm
Next, we calculate the volume of the outer cylinder (V_outer) and the inner cylinder (V_inner):
V_outer = π * (External radius)² * Height = π * (4 cm)² * 21 cm
V_inner = π * (Internal radius)² * Height = π * (3 cm)² * 21 cm
Now, the volume of the iron used to make the pipe is the difference between V_outer and V_inner:
V_iron = V_outer - V_inner
The weight of the iron pipe can be calculated by multiplying the volume with the density of iron:
Weight = V_iron * Density of iron = V_iron * 8 g/cm³
Substituting the values and calculating:
Weight = (V_outer - V_inner) * 8 g/cm³
Weight ≈ 3.696 kg
Therefore, the weight of the pipe is approximately 3.696 kg, which corresponds to option b.
Understanding the concepts of volume, density, and geometry allows us to calculate the weight of complex shapes like this hollow iron pipe accurately. This type of calculation has applications in various industries, including construction, engineering, and materials science.
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