Video Transcript
Find an expression for the shaded
cross-sectional area of the following rectangular prism.
In this question, we want to find
an expression for the cross-sectional area of a given rectangular prism. To do this, we are given an
expression for the volume of the prism and an expression for its height.
We can begin by recalling that the
volume of a prism is given by the area of its cross section multiplied by its
height. We can substitute the given
expressions for the volume and height into the formula for the volume of a prism to
obtain 240π¦π§ squared is equal to π times 15π¦. We want to find the cross-sectional
area π. So, we will need to divide both
sides of the equation through by 15π¦. This gives us that π is equal to
240π¦π§ squared over 15π¦, where we note that π¦ is nonzero.
We can now cancel the shared factor
of 15 and the shared factor of π¦ in the numerator and denominator. This gives us that the
cross-sectional area of the given rectangular prism is 16π§ squared.
