To find the area of the label needed for the can of olives, we need to calculate the surface area of the side (lateral area) of the cylinder, as well as the area of the top and bottom (circular areas).
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Calculate the radius of the can:
- Diameter = 6 inches
- Radius (r) = Diameter / 2 = 6 inches / 2 = 3 inches
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Calculate the lateral surface area:
- The formula for the lateral surface area of a cylinder is: \[ Lateral , Area = 2 \pi r h \]
- Where \( h \) is the height of the cylinder.
- Here, \( r = 3 \) inches and \( h = 4 \) inches.
- Plugging in the values: \[ Lateral , Area = 2 \times 3.14 \times 3 \times 4 = 2 \times 3.14 \times 12 = 75.36 , \text{square inches} \]
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Calculate the area of the top and bottom:
- The area of one circle is: \[ Area , of , Circle = \pi r^2 \]
- For the top and bottom combined: \[ Area , of , Top , and , Bottom = 2 \times \pi r^2 = 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52 , \text{square inches} \]
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Total surface area needed for the label:
- Total Area = Lateral Area + Area of Top and Bottom: \[ Total , Area = 75.36 + 56.52 = 131.88 , \text{square inches} \]
Thus, the total area of paper needed for the label on the outside of the can is 131.88 square inches.
The correct response is 131.88.