To calculate the amount of paper needed for the label on the outside of a cylindrical can of olives, we need to find the lateral surface area of the cylinder. The formula for the lateral surface area \( A \) of a cylinder is:
\[ A = 2\pi r h \]
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:
\[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches} \]
- The height \( h \) of the can is 4 inches.
Now, we can substitute the values into the formula using \( \pi \approx 3.14 \):
\[ A = 2 \times 3.14 \times 3 \times 4 \]
Calculating step-by-step:
-
Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]
-
Calculate \( 6.28 \times 3 \): \[ 6.28 \times 3 = 18.84 \]
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Finally, calculate \( 18.84 \times 4 \): \[ 18.84 \times 4 = 75.36 \]
Therefore, the area of the label needed for the can of olives is 75.36 square inches.
The answer is: 75.36.