$A B:$ Adiabatic compression,

$V_{A}=V_{1}, V_{B}=1 \,m ^{3}$

$B C:$ Isothermal expansion,

$V_{C}=V=10 \,m ^{3}$

$C D$ : Adiabatic expansion,

$V_{D}=V_{3}$

$D A$ : Isothermal compression,

$V_{A}=V_{1}$

Cycle efficiency is given, $\eta=\frac{3}{4}$

For given Carnot's cycle,

$\eta=1-\frac{T_{1}}{T_{2}}=1-\left(\frac{V_{2}}{V_{1}}\right)^{\gamma-1}$

$[\therefore$ Process $A B$ is adiabatic, $\gamma=\frac{5}{3}$ for monoatomic gas]

$\Rightarrow \quad \frac{3}{4}=1-\left(\frac{1}{V_{1}}\right)^{\frac{5}{3}-1} \Rightarrow \frac{1}{V_{1}^{2 / 3}}=\frac{1}{4}$

$\Rightarrow V_{1}=8 \,m ^{3}$