Answer
$\dfrac{ 16 \sqrt 2}{3} m^3$
Work Step by Step
We have the area of an equilateral triangle is: $A(x)=(\sqrt 2 x)^2 =2 x^2$
The volume of a solid can be computed as:
$V=\int_a^b A(y) dy=\int_a^{4 \sqrt {2/3}} \dfrac{3 \sqrt 3 x^2}{8} \ dx \\=\dfrac{3 \sqrt 3}{8} [\dfrac{x^3}{3}]_0^{\sqrt {\frac{2}{3}}} \\=\dfrac{ 16 \sqrt 2}{3} m^3$
