Answer
The new volume is $997.5cm^3$
Work Step by Step
We can solve for the change in volume using the following formula:
$\frac{\Delta V}{V_0}=-\frac{1}{B}\Delta P$
$\frac{\Delta V}{1000cm^3(1m/100cm)^3}=-\frac{1}{B_{alcohol}}(2.6*10^6N/m^2-1.0*10^5N/m^2)$
$\Delta V=-\frac{1}{B_{alcohol}}(2.6*10^6N/m^2-1.0*10^5N/m^2)*1000cm^3(1m/100cm)^3$
$\Delta V=-\frac{1}{1.0*10^9N/m^2}(2.6*10^6N/m^2-1.0*10^5N/m^2)*1000cm^3(1m/100cm)^3$
$\Delta V=-2.5*10^{-6}m^3$ or $-2.5cm^3$
Then;
$V=V_0+\Delta V$
$V=1000cm^3+-2.5cm^3=997.5cm^3$
The new volume is $997.5cm^3$.