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To calculate the volume of a cylinder, the formula used is:

\[
V = \pi r^2 h
\]

Where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.

### Step-by-step calculation:
1. **Given**: Diameter of the cylinder = 10.6 cm, so the radius \( r \) is half of the diameter:
   \[
   r = \frac{10.6}{2} = 5.3 \text{ cm}
   \]
2. **Height** of the cylinder \( h = 7.8 \text{ cm} \).

3. **Substitute** these values into the volume formula:
   \[
   V = \pi (5.3)^2 (7.8)
   \]

4. First, calculate the square of the radius:
   \[
   5.3^2 = 28.09 \text{ cm}^2
   \]

5. Then, multiply by the height:
   \[
   28.09 \times 7.8 = 219.102 \text{ cm}^3
   \]

6. Now, multiply by \( \pi \) (using \( \pi \approx 3.1416 \)):
   \[
   V \approx 219.102 \times 3.1416 = 688.320 \text{ cm}^3
   \]

7. **Round** to one decimal place:
   \[
   V \approx 688.3 \text{ cm}^3
   \]

### Final Answer:
The volume of the cylinder is approximately **688.3 cm³**.

Would you like further details or have any questions?

Here are five related questions for you:
1. How would the volume change if the height doubled?
2. What if the diameter was reduced by 20%? What would the new volume be?
3. How is the volume affected by increasing both the diameter and height by a factor of 1.5?
4. How can you derive the surface area of the cylinder from the given dimensions?
5. What is the volume of a similar cylinder with a radius of 6 cm and height of 10 cm?

**Tip**: Always ensure you use the radius, not the diameter, when calculating the volume of a cylinder!

Find the volume of the cylinder with a diameter of 10.6 cm and height of 7.8 cm, as shown in the diagram below. Give your answer correct to 1 decimal place.

Calculate the volume of a cylinder with a diameter of 10.6 cm and height of 7.8 cm. Learn how to apply the formula V = πr²h to solve this problem, suitable for Grades 7-9. The final answer is approximately 688.3 cm³.

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