To determine the surface area of the label needed for the outside of the can of olives, we need to calculate the lateral surface area of the cylindrical can, which is given by the formula:
\[ \text{Lateral Surface Area} = 2 \pi r h \]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Step 1: Find the radius
The diameter of the can is 6 inches, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
Step 2: Use the height
The height \( h \) of the can is given as 4 inches.
Step 3: Calculate the lateral surface area
Now we can plug values into the formula:
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 3 \times 4 \]
Step 4: Perform the calculations
First, calculate \( 2 \times 3.14 \):
\[ 2 \times 3.14 = 6.28 \]
Now, calculate \( 6.28 \times 3 \):
\[ 6.28 \times 3 = 18.84 \]
Finally, calculate \( 18.84 \times 4 \):
\[ 18.84 \times 4 = 75.36 \]
Conclusion
The amount of square inches of paper needed for the label on the outside of the can is 75.36 square inches.
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