1.7
MODELING WITH FUNCTIONS
Who was the
roundest knight at
King Arthur's
Round Table?
Sir Cumference
From Words to Expressions
 A number increased by 2 then cut in half
 5 decreased by a number then tripled
 A number decreased by 7 then doubled
Area of a Circle
 We know….
Area=πr²
 But….
What happens when we have the
circumference and we have to find area???
 Well….
Area of Circle Cont.
 C= Circumference
 Since C= 2πr we can solve for r to get r=
C/(2π). Then we can substitute to get area: A=
πr²= π(C/2 π))²= πC²/(4π²)= C²/(4π)
 So …
Area= C²/(4π)
 Example: C= 8 so 8²/(4π)= 5.093
Box Problem
 A square of side X is cut out of each corner of
an 8 in. by 15 in. piece of cardboard and the
sides are folded up to form an open-topped
box. How big should the cut-out squares be
in order to produce the box of maximum
volume?
8
x
x
15
Solution
 Volume = Length x Width x Height
 V = (15-2x) (8-2x) (x)
 X = 1.667 inches
Box Problem 2
 A square side is cut out of each corner from a
20cm by 8cm piece of cardboard to form an
open-top box. Find the value of x for the box
to have the maximum amount of volume.
Solution
 Volume = Length x Width x Height
 V = (8-2x) (20-2x) (x)
 X = 1.761 centimeters
Box Problem 3
 Find the maximum volume.
10
X
X
47
Solution
 Volume = Length x Width x Height
 V = (10-2x) (47-2x) (x)
 V = 526.847 units