To determine the total engine displacement, we use the formula that involves the following parameters:
- [tex]\(\pi\)[/tex], which is a mathematical constant approximately equal to 3.14159.
- [tex]\(r\)[/tex], the radius of the cylinder bore.
- [tex]\(\text{stroke}\)[/tex], the distance the piston travels within the cylinder.
- [tex]\(\text{number of pistons}\)[/tex], the total number of pistons within the engine.
Step-by-step:
1. First, compute the area of the cylinder bore cross-section, which is a circle. The formula for the area of a circle is [tex]\(\pi r^2\)[/tex], where [tex]\(r\)[/tex] is the radius.
2. Next, multiply this cross-sectional area by the stroke length to compute the volume for one cylinder. Hence, [tex]\(\pi r^2 \times \text{stroke}\)[/tex].
3. Finally, multiply this volume by the number of pistons in the engine to obtain the total engine displacement.
Thus, the correct formula for determining the total engine displacement is:
[tex]\[ \pi r^2 \times \text{stroke} \times \text{number of pistons} \][/tex]
So, the correct option is:
[tex]\[ \pi r^2 \times \text{stroke} \times \text{number of pistons} \][/tex]
