To find the square inches of paper needed for the label on the outside of the can, we will calculate the lateral surface area of the cylinder (the can).
The formula for the lateral surface area (A) of a cylinder is given by: \[ A = 2 \pi r h \] Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder
Given:
- The diameter of the can is 6 inches, so the radius \( r \) is: \[ r = \frac{6}{2} = 3 \text{ inches} \]
- The height \( h \) is given as 4 inches.
Now, substituting the values into the formula: \[ A = 2 \times 3.14 \times 3 \times 4 \] \[ A = 2 \times 3.14 \times 12 \] \[ A = 6.28 \times 12 \] \[ A = 75.36 \text{ square inches} \]
Thus, the amount of paper needed for the label on the outside of the can is 75.36 square inches.
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