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To determine the surface area of the can of tomato paste, we need to calculate the surface area of a cylinder, which consists of the area of the two circular ends and the rectangular side that wraps around the can.

Given:
- Radius of the can (\( r \)) = 1.2 inches
- Height of the can (\( h \)) = 3.4 inches

The formula for the surface area \( S \) of a cylinder is:
\[
S = 2\pi r^2 + 2\pi r h
\]
where:
- \( 2\pi r^2 \) represents the area of the two circular bases.
- \( 2\pi r h \) represents the area of the side (the rectangle that wraps around the can).

Let's calculate this step by step:

1. **Calculate the area of the circular ends:**
   \[
   2\pi r^2 = 2 \times \pi \times (1.2)^2
   \]
   \[
   = 2 \times \pi \times 1.44
   \approx 9.05 \, \text{square inches}
   \]

2. **Calculate the area of the side:**
   \[
   2\pi r h = 2 \times \pi \times 1.2 \times 3.4
   \]
   \[
   = 2 \times \pi \times 4.08
   \approx 25.63 \, \text{square inches}
   \]

3. **Add the two areas together to find the total surface area:**
   \[
   S \approx 9.05 + 25.63
   \]
   \[
   S \approx 34.7 \, \text{square inches}
   \]

Therefore, the surface area of the can is approximately **34.7 square inches**.

Would you like further details, or do you have any questions?

Here are some related questions for further exploration:
1. What would the surface area be if the height were doubled?
2. How does the surface area change if the radius increases to 1.5 inches?
3. What is the formula for the volume of a cylinder, and how does it apply here?
4. How would using a different unit of measurement (e.g., centimeters) affect the calculations?
5. Can you derive the formula for the surface area of a cylinder?

**Tip:** Remember that understanding how to apply formulas for basic shapes is crucial in solving real-world geometry problems.

Determine the amount of steel needed for the can of tomato paste. Use the π button on the calculator. Round to the nearest tenth of a unit.

Learn how to determine the surface area of a cylindrical can with a radius of 1.2 inches and height of 3.4 inches. This step-by-step solution shows how to apply the surface area formula for cylinders and round the answer to the nearest tenth.

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