To calculate the surface area of the label needed for the can of olives, we need to find the lateral surface area of the cylinder as well as the area of the top and bottom. The can is a cylinder with a diameter of 6 inches and a height of 4 inches.
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Calculate the radius: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
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Calculate the lateral surface area: The lateral surface area of a cylinder is given by the formula: \[ \text{Lateral Surface Area} = 2 \pi r h \] Plugging in the values: \[ \text{Lateral Surface Area} = 2 \times 3.14 \times 3 \times 4 = 75.36 \text{ square inches} \]
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Calculate the area of the top and bottom: The area of the top (and bottom) of a cylinder is given by the formula: \[ \text{Area of a circle} = \pi r^2 \] So, the area of the top and bottom combined is: \[ \text{Total Area of Top and Bottom} = 2 \times \pi r^2 = 2 \times 3.14 \times 3^2 = 2 \times 3.14 \times 9 = 56.52 \text{ square inches} \]
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Total surface area needed for the label: \[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of Top and Bottom} \] \[ \text{Total Surface Area} = 75.36 + 56.52 = 131.88 \text{ square inches} \]
Therefore, the total amount of paper needed for the label on the outside of the can is 131.88 square inches. So the correct response is 131.88.