What is the Volume of a Hershey Kiss Using Calculus?

[dude1it]

Volume of a Hershey Kiss!

Homework Statement

Alright, so me and my lab partner need to use calculus to find the volume of a hershey kiss...

We will take the slope of the side, and rotate it around the x-axis by finding the integral to find the volume...only problem is, we don't know the slope equation for the hershey kiss! Any help?

We need the same diameter of the base...

Homework Equations

Integral equation for revolution by x axis

Need limits

The Attempt at a Solution

We need to find the slope first...

So far we found the most similar equation to be x=y^y

 

[Integral]

Measure it. What is the radius of the base? How tall is it? Drawing a picture is always important.

 

[dude1it]

Measure it. What is the radius of the base? How tall is it? Drawing a picture is always important.

measured it, plotted points on graphing cal...looked like a straight line, not a curve

 

[LCKurtz]

You don't need a slope because it varies; Hershey's kisses don't look like cones.

Try modeling it with something something like this around the y=axis after scaling it properly:

$$y = 1 + (1-x)^{\frac 1 3} - x^{\frac 1 3}$$

 

[dude1it]

You don't need a slope because it varies; Hershey's kisses don't look like cones.

Try modeling it with something something like this around the y=axis after scaling it properly:

$$y = 1 + (1-x)^{\frac 1 3} - x^{\frac 1 3}$$

Eh I'm sorry, I meant derivative...we'll take the integral volume equation of the derivative

 

[dude1it]

Hershey's website lists the weight as 41 grams per 9 pieces, so one Kiss weighs 41/9 grams, or 4.55 grams. Since 1 gram is 1/454 of a pound, each kiss weighs 4.55/454 pounds, or 1/100 pound. That's your mass.

The shape of a Kiss is a cone, which requires two measurements, radius and height.

According to the marylandmommy site, the diameter of the base of a Kiss is .819 inches, and the height is the same as the diameter.

So radius is .819/2 or 0.4095 inches, and height is .819 inches.

The formula for the volume of a cone is (1/3) * pi * r^2 * h, where r is radius and h is height. Plug in your measurements and do the arithmetic:

Volume = (1/3) * 3.1416 * .4095*.4095 * .819
Volume=0.143820683 cubic inches

there ... but i need it in calculus buds.

should i just use y=x^(-x) and get the integral of it with limits from .25 - 2.25.

let me know

 

[LCKurtz]

You don't need a slope because it varies; Hershey's kisses don't look like cones.

Try modeling it with something something like this around the y=axis after scaling it properly:

$$y = 1 + (1-x)^{\frac 1 3} - x^{\frac 1 3}$$

Just to whet your appetite, here's a picture of what this looks like if you revolve it:

[PLAIN]http://math.asu.edu/~kurtz/pix/ChocolateChip.jpg