To find the area of paper needed for the label on the outside of the can, we need to calculate the lateral surface area of the cylinder (the can). The formula for the lateral surface area \( A \) of a cylinder is:
\[ A = 2\pi rh \]
Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant (approximately 3.14).
Step 1: Find the radius of the can.
The diameter of the can is given as 2.5 inches, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{2.5}{2} = 1.25 \text{ inches} \]
Step 2: Identify the height of the can.
The height \( h \) is given as 3.5 inches.
Step 3: Plug the values into the formula.
Now we can use the lateral surface area formula:
\[ A = 2\pi rh \] Substituting in the values we found:
\[ A = 2 \times 3.14 \times 1.25 \times 3.5 \]
Step 4: Calculate the area.
First, we calculate \( 2 \times 3.14 = 6.28 \).
Next, calculate \( 1.25 \times 3.5 = 4.375 \).
Now, multiply these two results:
\[ A = 6.28 \times 4.375 \]
Calculating \( 6.28 \times 4.375 \):
\[ A \approx 27.515 \]
Step 5: Round to the nearest inch.
Now, we round 27.515 to the nearest inch:
\[ \text{Rounded Area} \approx 28 \text{ square inches} \]
Final Answer:
The label on the outside of the can will require approximately 28 square inches of paper.