What is the total displacement in **litres** of a 4-cylinder petrol engine with a bore of 89 mm diameter and a stroke of 83 mm.   Change to cm before calculating. (1000 cc = 1 litre)

**Note:**  The volume of one cylinder is found by the distance a piston
                        moves in one stroke.

To calculate the total displacement of a 4-cylinder engine, we first need to determine the displacement (volume) of one cylinder and then multiply it by the number of cylinders.

### Step 1: Convert dimensions from millimeters to centimeters
Given:
- Bore (diameter, \(d\)) = 89 mm = 8.9 cm
- Stroke (\(s\)) = 83 mm = 8.3 cm

### Step 2: Calculate the volume of one cylinder
The volume of a cylinder \(V\) is given by:

\[
V = \pi \times \left(\frac{d}{2}\right)^2 \times s
\]

Where:
- \(d\) is the bore (diameter)
- \(s\) is the stroke
- \(\pi\) (Pi) is approximately 3.14159

Substituting the values:

\[
V = 3.14159 \times \left(\frac{8.9 \, \text{cm}}{2}\right)^2 \times 8.3 \, \text{cm}
\]

### Step 3: Calculate the displacement for one cylinder
Let's calculate:

\[
V = 3.14159 \times \left(4.45 \, \text{cm}\right)^2 \times 8.3 \, \text{cm}
\]

\[
V \approx 3.14159 \times 19.8025 \, \text{cm}^2 \times 8.3 \, \text{cm}
\]

\[
V \approx 3.14159 \times 164.36175 \, \text{cm}^3
\]

\[
V \approx 516.105 \, \text{cm}^3
\]

So, the volume of one cylinder is approximately 516.105 cubic centimeters (cc).

### Step 4: Calculate the total displacement for 4 cylinders
Since the engine has 4 cylinders:

\[
\text{Total Displacement} = 4 \times 516.105 \, \text{cm}^3
\]

\[
\text{Total Displacement} \approx 2064.42 \, \text{cm}^3
\]

### Step 5: Convert the total displacement to liters
Since 1000 cc = 1 liter:

\[
\text{Total Displacement in Liters} \approx \frac{2064.42 \, \text{cm}^3}{1000} \approx 2.064 \, \text{liters}
\]

So, the total displacement of the engine is approximately **2.064 liters**.

Do you have any questions or want more details?

Here are 5 related questions for further exploration:
1. How would the total displacement change if the engine had 6 cylinders instead of 4?
2. What effect does increasing the bore diameter have on engine displacement?
3. How does the stroke length impact the engine's power and torque?
4. What is the difference between engine displacement and engine power?
5. How would you calculate the displacement for an engine with a variable stroke length?

**Tip:** When dealing with engine displacement, remember that increasing either the bore or the stroke will increase the overall engine displacement, leading to a potentially more powerful engine.

Learn how to calculate the total displacement of a 4-cylinder petrol engine using cylinder volume calculations. Detailed steps include converting dimensions, applying the cylinder volume formula, and converting cubic centimeters to liters. Ideal for automotive enthusiasts and students studying geometry and trigonometry.

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