To calculate the surface area of the label needed for the outside of the can, we need to find the lateral surface area of the can (which is a cylinder) and the area of the top and bottom of the can.
The formulas we will use are:
-
Lateral surface area of the cylinder: \[ A_{\text{lateral}} = 2 \pi r h \]
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Area of the top and bottom circles: \[ A_{\text{top and bottom}} = 2 \pi r^2 \]
Given:
- Diameter of the can = 6 inches
- Height of the can = 4 inches
First, we find the radius: \[ r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
Now we can calculate the lateral surface area: \[ A_{\text{lateral}} = 2 \pi r h = 2 \times 3.14 \times 3 \times 4 \] \[ A_{\text{lateral}} = 2 \times 3.14 \times 12 = 75.36 \text{ square inches} \]
Next, we find the area of the top and bottom: \[ A_{\text{top and bottom}} = 2 \pi r^2 = 2 \times 3.14 \times 3^2 \] \[ A_{\text{top and bottom}} = 2 \times 3.14 \times 9 = 56.52 \text{ square inches} \]
Now, we sum these two areas to find the total surface area: \[ A_{\text{total}} = A_{\text{lateral}} + A_{\text{top and bottom}} = 75.36 + 56.52 = 131.88 \text{ square inches} \]
Thus, the total square inches of paper needed for the label on the outside of the can is 131.88.
The answer is: 131.88