The value of $500 \text{ cc}$ represents the total volume ($V_{tot}$) of one cylinder when the piston is at its lowest point (Bottom Dead Center, BDC). This total volume is the sum of the swept volume ($V_s$) and the clearance volume ($V_c$). The compression ratio ($CR$) is given as $10:1$. The compression ratio is defined as: $$CR = \frac{\text{Total Volume}}{\text{Clearance Volume}} = \frac{V_s + V_c}{V_c}$$ From this definition, we can also express the swept volume ($V_s$) in terms of the total volume ($V_{tot}$) and the compression ratio ($CR$). We know that $V_{tot} = V_s + V_c$. From the compression ratio definition: $$CR = \frac{V_{tot}}{V_c} \implies V_c = \frac{V_{tot}}{CR}$$ Now substitute $V_c$ back into the equation for $V_{tot}$: $$V_{tot} = V_s + \frac{V_{tot}}{CR}$$ Rearrange to solve for $V_s$: $$V_s = V_{tot} - \frac{V_{tot}}{CR}$$ $$V_s = V_{tot} \left(1 - \frac{1}{CR}\right)$$ $$V_s = V_{tot} \left(\frac{CR - 1}{CR}\right)$$ Given: $V_{tot}$ per cylinder = $500 \text{ cc}$ (from the previous step, $2 \text{ litres} / 4 \text{ cylinders} = 0.5 \text{ litres} = 500 \text{ cc}$) $CR = 10$ Substitute these values into the formula for $V_s$: $$V_s = 500 \text{ cc} \times \left(\frac{10 - 1}{10}\right)$$ $$V_s = 500 \text{ cc} \times \left(\frac{9}{10}\right)$$ Therefore, $\frac{9}{10}$ is used to multiply $500 \text{ cc}$ to calculate the swept volume ($V_s$) per cylinder, which is the volume displaced by the piston as it moves from Bottom Dead Center (BDC) to Top Dead Center (TDC).