# 2.7 – Mathematical Modeling ```2.7 – Mathematical Modeling
MODELING VOLUME
An open box with a square base is to be cut from a square piece of cardboard with side equal to 18 inches but
cutting out a square from each corner and turning up the sides.
Draw a Diagram:
Write the volume, V, of the box as a function of
the length x of the square cut from the box. Write in
standard form:
For what value of x is the volume the largest? What is the largest possible volume?
MODELING AREA
A farmer has 3000 feet of fencing to enclose a rectangular field. One side lies along a river, so only three sides
need fencing.
Draw a diagram:
Express the area A of the field enclosed by the fence
as function of l, the length of the side parallel to the
river.
For what value of l is the area the largest? What is the largest area?
A rectangle is inscribed in a semicircle of radius 2. Let P = (x, y) be the point
in Quadrant I that is a vertex of the rectangle and is on the circle.
Express the area A of the rectangle as a function of x.
Express the perimeter P as a function of x.
For what value of x is A the largest? How about P?
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