Final Answer:
The dimensions of the storage unit are
in height, ensuring a volume of
By solving the cubic equation and considering the meaningful root
these dimensions fulfill the specified volume requirement.
Step-by-step explanation:
The rectangular prism representing the storage unit is characterized by dimensions expressed in terms of the variable
The volume of this prism, crucially important for storage capacity, is specified as
. Setting up the volume equation,
, we embark on the process of simplification, ultimately leading to a cubic equation.
Through factoring, we discern two potential solutions for
one of which proves relevant in the context of the problem
The cubic expression is factored into
, elucidating the significance of
as a root.
By substituting this value back into the expressions denoting length, width, and height, we unveil the conclusive dimensions of the storage unit:
in width, and
in height. Consequently, the storage unit, with its dimensions of
feet, satisfies the stipulated volume requirement of
thereby offering an optimal solution for effective storage space.