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The problem involves calculating the total surface area of a cylindrical tube. The given dimensions are:

- Radius (\( r \)) = 2.2 cm
- Length/height (\( h \)) = 10 cm

### Surface area of a cylinder:
The total surface area of a closed cylinder consists of two parts:
1. **Lateral surface area**: The area around the side of the cylinder.
   \[
   \text{Lateral area} = 2\pi r h
   \]
2. **Area of the two circular ends** (top and bottom):
   \[
   \text{Area of both ends} = 2\pi r^2
   \]

### Total surface area:
\[
\text{Total surface area} = 2\pi r h + 2\pi r^2 = 2\pi r (h + r)
\]

### Substituting the values:
- \( r = 2.2 \, \text{cm} \)
- \( h = 10 \, \text{cm} \)

\[
\text{Total surface area} = 2\pi (2.2) (10 + 2.2)
\]
\[
\text{Total surface area} = 2\pi (2.2) (12.2)
\]
\[
\text{Total surface area} = 2 \times 3.1416 \times 2.2 \times 12.2
\]
\[
\text{Total surface area} \approx 168.89 \, \text{cm}^2
\]

So, the total surface area of the tube is approximately **168.89 cm²**.

Would you like further details or clarification?

Here are 5 related questions to deepen your understanding:
1. How would the surface area change if the radius of the cylinder were doubled?
2. What is the formula for the volume of a cylinder, and how would you apply it here?
3. How would you calculate the surface area if the tube was hollow?
4. Can you derive the lateral surface area of a cone using a similar approach?
5. How do different units (cm, m, mm) affect surface area calculations?

**Tip:** Always ensure that the radius and height are in the same units before applying the surface area formula.

The diagram shows a tube containing chocolate sweets. Calculate the total surface area of the tube.

Learn how to calculate the total surface area of a cylindrical tube with a radius of 2.2 cm and height of 10 cm. This problem involves using the surface area formula for cylinders and applying it to find a total surface area of approximately 168.89 cm². Perfect for Grades 6-8 geometry students.

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