$$ rac{{2pi }}{{15}}$$
$$ rac{{3pi }}{{16}}$$
$$ rac{{3pi }}{8}$$
$$ rac{pi }{{16}}$$
Answer is Right!
Answer is Wrong!
The correct answer is $\boxed{\frac{{3\pi }}{8}}$.
The section modulus is a measure of the ability of a beam to resist bending. It is defined as the second moment of area of the cross-section divided by the distance from the neutral axis to the extreme fiber.
The section modulus of a square section of side $B$ is given by:
$$S_s = \frac{{B^3}}{12}$$
The section modulus of a circular section of diameter $D$ is given by:
$$S_c = \frac{{\pi D^3}}{32}$$
The ratio of the section modulus of a square section of side $B$ and that of a circular section of diameter $D$ is therefore:
$$\frac{{S_s}}{{S_c}} = \frac{{\frac{{B^3}}{12}}}{{\frac{{\pi D^3}}{32}}} = \frac{{12}}{{\pi D}} = \frac{{12}}{{3.14 \times 2}} = \frac{{3\pi }}{8}$$