To calculate the surface area needed for the label on the outside of a cylindrical can of olives, we will consider the lateral surface area of the cylinder (the height and the circumference).
The formula for the lateral surface area of a cylinder is: \[ \text{Lateral Surface Area} = 2 \pi r h \]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Diameter of the can = 6 inches, so the radius \( r = \frac{6}{2} = 3 \) inches.
- Height \( h = 4 \) inches.
- Using \( \pi \approx 3.14 \).
Now we can plug in the values:
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 3 \times 4 \] \[ = 2 \times 3.14 \times 12 \] \[ = 2 \times 37.68 \] \[ = 75.36 \]
So the amount of square inches of paper needed for the label is approximately 75.36 square inches.
The closest option from the choices provided (75.26, 131.88, 150.72, 376.8) would be 75.26 square inches.