B2. We want to make a pot without a lid in the shape of a cube with an edge of $30 \mathrm{~cm}$.

A. What is the minimum amount of $\mathrm{m}^{2}$ of sheet metal needed for its manufacture?

B. How long in mm is the longest possible straight thin invisible rod that can be placed in the pot?

C. How many liters does the pot hold?
B2. The surface area of the cube without the cover $P=5 a^{2}=4500 \mathrm{~cm}^{2}=0.45 \mathrm{~m}^{2}$. The rod is placed in the position of the body diagonal $z$ with a length of $D=\sqrt{3 a^{2}} \approx 519 \mathrm{~mm}$. The volume of the cube $V=a^{3}=27000 \mathrm{~cm}^{3}=$ 271.

A. The calculated smallest surface area $P=4500 \mathrm{~cm}^{2}$. ............................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_3ad088fae533eb6a81abg-7.jpg?height=57&width=1602&top_left_y=1885&top_left_x=313)

![](https://cdn.mathpix.com/cropped/2024_06_07_3ad088fae533eb6a81abg-7.jpg?height=60&width=1664&top_left_y=1946&top_left_x=253)

![](https://cdn.mathpix.com/cropped/2024_06_07_3ad088fae533eb6a81abg-7.jpg?height=51&width=1602&top_left_y=2002&top_left_x=313)

C. The cube holds 27 liters. ......................................................................................................