B2. From an oak log with a diameter of $d=40 \mathrm{~cm}$, we want to cut out the largest beam with a square cross-section with a side length of $a$, as shown in the cross-sectional diagram. The length of the log (and the beam) is $4 \mathrm{~m}$.

A Calculate the length of the side of the beam, denoted by $a$.

Write the result in centimeters to one decimal place.

B Calculate the volume of the beam in cubic meters to three decimal places.

![](https://cdn.mathpix.com/cropped/2024_06_07_fb8dcc2580df7ec25528g-4.jpg?height=348&width=354&top_left_y=1294&top_left_x=1565)
accurately.

C Calculate the volume of the log to the nearest thousandth of a cubic meter (use the value 3.14 for $\pi$).
B2. To calculate the length of the diagonal of the square, we use the Pythagorean theorem: $40^{2}=a^{2}+a^{2}$. The side length a is $28.3 \, \text{cm}$.

B The volume of the square prism is $V_{t}=a^{2} \cdot l=(28.3)^{2} \cdot 400=320356 \, \text{cm}^{3}=0.320 \, \text{m}^{3}$.

C The volume of the cylinder is $V_{d}=\pi r^{2} \cdot l=3.14 \cdot 20^{2} \cdot 400=502400 \, \text{cm}^{3}=0.502 \, \text{m}^{3}$.