1.7

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

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 x x

Solution  Volume = Length x Width x Height  V = (15-2x) (8-2x) (x)  X = 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 = centimeters

Box Problem 3  Find the maximum volume X X

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