MODELING WITH FUNCTIONS1.7

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

(n+2)/2 3(5-n)

2(n-7)

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

15

xx

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

47

XX

Solution

Volume = Length x Width x Height V = (10-2x) (47-2x) (x)

V = 526.847 units