Correct Answer - Option 3 : 9.38

**Concept:**

**Compression ratio (r):**

It is defined as the** ratio of the sum of clearance volume and swept volume to the clearance volume.**

It is given by

\({\bf{r}} = \frac{{{{\bf{v}}_{\bf{c}}} + {{\bf{v}}_{\bf{s}}}}}{{{{\bf{v}}_{\bf{c}}}}} = \frac{{{{\bf{v}}_1}}}{{{{\bf{v}}_2}}}\)

where

\({{\bf{v}}_{\bf{s}}} = Swept ~volume= \;\frac{{\bf{\pi }}}{4}\; × \;{{\bf{d}}^2}\; × \;{\bf{l}}\times n\)

**Calculation:**

**Given:**

Number of cylinder (n) = 6, bore (d) = 20 cm, stroke length (l) = 40 cm, v_{c} = 2000 cm^{3}, r = ?

Now, we know that

Swept volume is:

\({{\bf{v}}_{\bf{s}}} = \;\frac{{\bf{\pi }}}{4}\; × \;{{\bf{d}}^2}\; × \;{\bf{l}}\times n\) = 0.7854 × 20^{2 }× 40 × 6

**∴ v**_{s} = 75398.22 cm^{3}

Compression ratio is:

\({\bf{r}} = \frac{{{{\bf{v}}_{\bf{c}}} + {{\bf{v}}_{\bf{s}}}}}{{{{\bf{v}}_{\bf{c}}}}}= \;\frac{{9000\; + \;75398.22}}{{9000}} \)

**∴ r = 9.38**