The volume 8

The volume of a right regular hexagonal prism is 187.2 cubic millimeters. The line segment that has a length of 2.6 millimeters begins at the center of the hexagon and ends at one side of the hexagon. 3 mm base. Find the height.

Correct answer:

h =  8 mm

Step-by-step explanation:

$$\begin{gathered} V=187.2{\text{mm}}^3 \\ {h}_2=2.6\text{mm} \\ a=3\text{mm} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{3\cdot 2.6}{2}=\frac{39}{10}=3.9{\text{mm}}^2 \\ {S}_6=6\cdot S_1=6\cdot 3.9=\frac{117}{5}=23.4{\text{mm}}^2 \\ V=S_6\cdot h \\ h=V/S_6=187.2/23.4=8\text{mm} \end{gathered}$$

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