hexagonal prisms with a volume of 1440 cm cubed

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem does not specify what is its request, hence, supposing that you need to evaluate the surface area of hexagonal prism, under the given conditions, yields:

`SA = 6ab + 6bh => SA = 6b(a + h)`

a represents the length of apothem of the hexagonal prism
b represents the length of base of the hexagonal prism.
h represents the height of the hexagonal prism

`BA = 3ab ` 

BA represents the base area of the prism

The problem provides the volume of the prism, such that:

`V = 3abh => 1440 = 3abh => 1440/h = 3ab => SA = 2*1440/h + 2*1440/a`

`SA = 2880(1/h + 1/a) => SA = 2880((a+h)/(ah))`

Hence, evaluating the surface area of the given hexagonal prism, under the given conditions, yields `SA = 2880((a+h)/(ah)).`