Honeycomb Cell Volume

A honeycomb is made up of cells that resemble a regular hexagonal 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.
a) How many liters of honey are there in the whole comb if the comb consists of 300 cells?
b) How many combs does a beekeeper need for 1 liter of honey?

Final Answer:

V =  0.08424 l
n₂ =  12

Step-by-step explanation:

$$\begin{gathered} a=3\text{mm} \\ {v}_1=2.6\text{mm} \\ h=12\text{mm} \\ n=300 \\ {V}_0=\frac{a\cdot v_1}{2}\cdot h=\frac{3\cdot 2.6}{2}\cdot 12=\frac{234}{5}=46.8{\text{mm}}^3 \\ {V}_1=6\cdot V_0=6\cdot \frac{234}{5}=\frac{6\cdot 234}{5}=\frac{1404}{5}=280.8{\text{mm}}^3 \\ {V}_2=n\cdot V_1=300\cdot \frac{1404}{5}=\frac{300\cdot 1404}{5}=\frac{421200}{5}=84240{\text{mm}}^3 \\ V=V_2\to \text{l}=V_2:1000000\text{l}=84240:1000000\text{l}=0.08424\text{l}=0.08424\text{l} \end{gathered}$$

$$\begin{gathered} V_3=1\text{l} \\ {n}_2=V_3/V=1/0.0842=12 \end{gathered}$$

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