To calculate the area of the paper needed for the label on the outside of the cylindrical can, we need to find the lateral surface area of the cylinder. 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:
- Diameter = 6 inches
Thus, the radius \( r = \frac{6}{2} = 3 \) inches. - Height \( h = 4 \) inches.
Substituting the values into the formula:
\[ A = 2 \pi (3) (4) \]
Using \( \pi \approx 3.14 \):
\[ A = 2 \times 3.14 \times 3 \times 4 \] \[ A = 2 \times 3.14 \times 12 \] \[ A = 2 \times 37.68 \] \[ A = 75.36 \text{ square inches} \]
So, the area of the paper needed for the label on the outside of the can is \( 75.36 \) square inches.
Answer: 75.36 square inches.