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Answer :
The weight of the hollow iron pipe is approximately 1.239 kg, and the closest option is A. 3.6 kg.
To find the weight of the hollow iron pipe, we need to determine its volume and then calculate the weight based on the density of iron.
1. Calculate the internal radius [tex](\(r_{\text{internal}})\)[/tex] of the pipe:
[tex]\[ r_{\text{internal}} = \frac{\text{external diameter}}{2} - \text{thickness} \][/tex]
[tex]\[ r_{\text{internal}} = \frac{8 \, \text{cm}}{2} - 1 \, \text{cm} = 3 \, \text{cm} \][/tex]
2. Calculate the internal volume [tex](\(V_{\text{internal}})\)[/tex] of the pipe:
[tex]\[ V_{\text{internal}} = \pi r_{\text{internal}}^2 \cdot \text{length} \][/tex]
[tex]\[ V_{\text{internal}} = \pi \cdot (3 \, \text{cm})^2 \cdot 21 \, \text{cm} \][/tex]
3. **Calculate the external volume [tex](\(V_{\text{external}})\)[/tex] of the pipe:**
[tex]\[ V_{\text{external}} = \pi (\text{external radius}^2 - r_{\text{internal}}^2) \cdot \text{length} \][/tex]
[tex]\[ V_{\text{external}} = \pi \cdot \left(\left(\frac{8 \, \text{cm}}{2}\right)^2 - (3 \, \text{cm})^2\right) \cdot 21 \, \text{cm} \][/tex]
4. Calculate the volume of the iron material [tex](\(V_{\text{iron}})\)[/tex] in the pipe:
[tex]\[ V_{\text{iron}} = V_{\text{external}} - V_{\text{internal}} \][/tex]
5. **Calculate the weight of the iron pipe:**
[tex]\[ \text{Weight} = \text{Density} \times V_{\text{iron}} \][/tex]
[tex]\[ \text{Weight} = 8 \, \text{g/cm}^3 \times V_{\text{iron}} \][/tex]
Now, perform the calculations to find the weight of the pipe and compare it with the given options.
Calculating the weight of the hollow iron pipe step by step:
1. Calculate [tex]\(r_{\text{internal}}\)[/tex]:
[tex]\[ r_{\text{internal}} = \frac{8 \, \text{cm}}{2} - 1 \, \text{cm} = 3 \, \text{cm} \][/tex]
2. Calculate [tex]\(V_{\text{internal}}\)[/tex]:
[tex]\[ V_{\text{internal}} = \pi \cdot (3 \, \text{cm})^2 \cdot 21 \, \text{cm} = 189 \pi \, \text{cm}^3 \][/tex]
3. Calculate [tex]\(V_{\text{external}}\)[/tex]:
[tex]\[ V_{\text{external}} = \pi \cdot \left(\left(\frac{8 \, \text{cm}}{2}\right)^2 - (3 \, \text{cm})^2\right) \cdot 21 \, \text{cm} = 345 \pi \, \text{cm}^3 \][/tex]
4. Calculate [tex]\(V_{\text{iron}}\)[/tex]:
[tex]\[ V_{\text{iron}} = V_{\text{external}} - V_{\text{internal}} = (345 - 189) \pi \, \text{cm}^3 = 156 \pi \, \text{cm}^3 \][/tex]
5. **Calculate the weight of the iron pipe:**
[tex]\[ \text{Weight} = 8 \, \text{g/cm}^3 \times 156 \pi \, \text{cm}^3 \approx 1239.44 \, \text{g} \][/tex]
Converting grams to kilograms:
[tex]\[ \text{Weight} \approx \frac{1239.44 \, \text{g}}{1000} \, \text{kg} \approx 1.239 \, \text{kg} \][/tex]
Therefore, the weight of the hollow iron pipe is approximately [tex]\(1.239 \, \text{kg}\)[/tex], and the closest option is A. [tex]\(3.6 \, \text{kg}\)[/tex].
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