Honeycomb capacity

The honeycomb comprises cells with the shape of a regular 6-sided prism with a base edge length of 3 mm and a corresponding height of 2.6 mm. The height of the prism is 12 mm. How many liters of honey are there in the entire comb if the plastic comprises approximately 300 cells? How much plastic does a beekeeper need for 1 liter of honey?

Final Answer:

V =  0.0842 l
n =  12

Step-by-step explanation:

$$\begin{gathered} a=3\text{mm} \\ {v}_1=2.6\text{mm} \\ h=12\text{mm} \\ {S}_1=a\cdot v_1/2=3\cdot 2.6/2=\frac{39}{10}=3.9{\text{mm}}^1 \\ {V}_1=6\cdot S_1\cdot h=6\cdot 3.9\cdot 12=\frac{1404}{5}=280.8{\text{mm}}^3 \\ {V}_2=300\cdot V_1=300\cdot 280.8=84240{\text{mm}}^3 \\ V=V_2\to \text{l}=V_2:1000000\text{l}=84240:1000000\text{l}=0.084\text{l}=0.0842\text{l} \end{gathered}$$

$$\begin{gathered} V_3=1\text{l} \\ {n}_1=V_3/V=1/0.0842\doteq 11.8708 \\ n=\lceil n_1\rceil =\lceil 11.8708\rceil =12 \end{gathered}$$

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