Your approach to finding the total surface area of the cylindrical container is generally correct. However, there is a small error in your calculations. Let's go through the steps together to ensure accuracy.
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Identify the dimensions:
- Diameter = 36 mm, so the radius \( r \) is: \[ r = \frac{36 \text{ mm}}{2} = 18 \text{ mm} \]
- Height \( h = 18 \text{ mm} \)
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Surface Area Formula: The formula for the total surface area \( S \) of a cylinder is: \[ S = 2\pi r (r + h) \]
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Plugging in the values: \[ S = 2 \times 3.14 \times 18 \times (18 + 18) \] Simplifying inside the parentheses: \[ S = 2 \times 3.14 \times 18 \times 36 \]
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Calculating step by step: First, calculate \( 18 \times 36 \): \[ 18 \times 36 = 648 \] Now plug this back into the expression: \[ S = 2 \times 3.14 \times 648 \] Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \] Now multiply by 648: \[ S = 6.28 \times 648 \] Performing the multiplication: \[ S \approx 4074.24 \text{ square millimeters} \]
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Final Result: The total surface area of the cylindrical container is approximately \( 4074.24 , \text{mm}^2 \).
Your initial calculation of \( 4069.92 \) mm² was slightly off. The correct surface area, when calculated accurately, is approximately \( 4074.24 \) square millimeters.