The Calculus Whiz Who Loved Candy Worksheet printable pdf download

The Calculus Whiz Who Loved Candy Worksheet

The Calculus Whiz Who Loved Candy

File Document #1

1. This is roughly the shape of a Hershey’s Kiss. The first thing I did is to

place part of a cross section on a graph grid and describe how to get this

solid by revolving it around an axis. (See #2)

2. I measured my candy and decided I could take the cross section

pictured on the left and rotate the region in the first quadrant about the

2 cm

y- axis and find the volume of the piece of candy by integration and the

method of shells.

3. I then had to write the equation of the region’s boundaries.

(This is an estimate.) I estimated that the equation of the curve

in the first quadrant was approximately:

(x - 1)

+1 , 0<x<1

f(x)=

2 cm

-(x -1)

+1 , 1<x<2

4. To graph f(x) on a graphing calculator, let

5. The region to be revolved about the y-axis is

= ( (x - 1)

+1) / ((x >0)*( x<1))

bounded by the curve f(x), and the lines x=0 and

= (- (x - 1)

+1) / ((x >1)*( x<2))

y=0.

6. I found the volume of the candy by the method of shells:

V =

x ((x - 1)

+1) dx

x (-(x - 1)

+1) dx

7. Let the graphing calculator give you the volume:

fnInt(2

x ((x - 1)

+1) , x , 0 , 1) = 3.66519

fnInt(2

x (-(x - 1)

+1) , x , 1 , 2) = 5.75959

The actual volume = 3.66519 + 5.75959= 9.42478 cm

Created by Linda Andereck Knowles, Santa Rosa School District

The Calculus Whiz Who Loved Candy Worksheet