To find the area of the label needed for the can of olives, we will need to calculate the lateral surface area and the area of the top and bottom of the can.
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Lateral Surface Area: The lateral surface area (A) of a cylinder is given by the formula: \[ A = 2 \pi r h \] where \( r \) is the radius and \( h \) is the height.
- The radius \( r \) is half of the diameter: \[ r = \frac{6 \text{ in}}{2} = 3 \text{ in} \]
- The height \( h \) is 4 inches.
- Using \( \pi \approx 3.14 \): \[ A = 2 \times 3.14 \times 3 \times 4 \] \[ A = 2 \times 3.14 \times 12 \] \[ A = 2 \times 37.68 = 75.36 \text{ square inches} \]
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Area of the Top and Bottom: The area of the top and bottom circles can be calculated using the formula for the area of a circle: \[ A_{circle} = \pi r^2 \]
- Area of one circle: \[ A_{circle} = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 \text{ square inches} \]
- Area of two circles (top and bottom): \[ A_{top , and , bottom} = 2 \times 28.26 = 56.52 \text{ square inches} \]
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Total Surface Area: Now, we can calculate the total area needed for the label: \[ A_{total} = A_{lateral} + A_{top , and , bottom} \] \[ A_{total} = 75.36 + 56.52 = 131.88 \text{ square inches} \]
Thus, the total area of paper needed for the label on the outside of the can is 131.88 square inches.
So, the correct response is 131.88.