To determine the amount of paper needed for the label on the outside of the can of olives, we will calculate the surface area of the cylindrical can (excluding the top and bottom surfaces since labels typically wrap around the sides).
The formula for the lateral surface area \( A \) of a cylinder is given by: \[ A = 2\pi rh \] where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
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Calculate the radius: The diameter of the can is given as 6 inches. Therefore, the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
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Use the height: The height \( h \) of the can is given as 4 inches.
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Substitute the values into the surface area formula: Using \( \pi \approx 3.14 \), we substitute \( r = 3 \) inches and \( h = 4 \) inches into the formula to find the lateral surface area: \[ A = 2 \times 3.14 \times 3 \times 4 \]
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Calculate: First, calculate the multiplication inside: \[ A = 2 \times 3.14 \times 3 \times 4 = 2 \times 3.14 \times 12 \] \[ = 2 \times 37.68 \] \[ = 75.36 \]
Thus, the amount of paper needed for the label on the outside of the can is 75.36 square inches.
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