\section*{Task 2 - 121022}

In the figure, a convex body bounded by planar surfaces is shown in top, front, and side views. The outlines of the depicted body are squares with side length \(a\) in all three views.

a) Draw the body in oblique parallel projection \(\left(\alpha=60^{\circ} ; q=\frac{1}{2}\right)\) for \(a=6 \mathrm{~cm}\).

b) Calculate the volume \(V\) of the body depicted in a)!

}

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-1315.jpg?height=693&width=902&top_left_y=316&top_left_x=583)
}

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-1315.jpg?height=505&width=443&top_left_y=1084&top_left_x=812)

The body is formed by cutting a pyramid with the base \(E F G H\) (where \(H\) is the point directly above \(A\), completing the cube) and height \(a\) out of a cube.

This results in the volume \(V\) of the body being

\[
V=V_{\text {cube }}-V_{\text {pyramid }}=a^{3}-\frac{1}{3} a \cdot a^{2}=\frac{2}{3} a^{3}=144 \mathrm{~cm}^{3}
\]