## Task B-3.5.

In the figure, there is a net of a geometric solid. Figures $A, E$, and $F$ are isosceles right triangles. Figures $B, C$, and $D$ are squares with side length 1, and $G$ is an equilateral triangle. Determine the volume of this solid.
## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_30_4b7629e40479ae2c2357g-22.jpg?height=922&width=952&top_left_y=1208&top_left_x=724)

Notice that the given net represents a geometric solid obtained by cutting off a regular triangular pyramid from a cube. (Points are awarded for a sketch or a precise description of the geometric solid)

The volume of this solid is calculated as the difference between the volume of the cube and the volume of the pyramid \( V = V_{\text{cube}} - V_{\text{pyramid}} \).

\[
\begin{gathered}
V_{\text{cube}} = a^3 = 1 \\
V_{\text{pyramid}} = \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot \frac{a^2}{2} \cdot a = \frac{a^3}{6} = \frac{1}{6}
\end{gathered}
\]

\[
V = 1 - \frac{1}{6} = \frac{5}{6}
\]