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## PowerPoint Slideshow about ' Arc Length and Surface Area' - sophia-rosales

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### Arc Length and Surface Area

### Surface Area

Compiled by Mrs. King

Start with something easy

The length of the line segment joining points (x0,y0) and (x1,y1) is

(x1,y1)

(x0,y0)

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

The Length of a Polygonal Path?

Add the lengths of the line segments.

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

The length of a curve?

Approximate by chopping it into polygonal pieces and adding up the lengths of the pieces

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

Approximate the curve with polygonal pieces?

www.spsu.edu/math/Dillon/2254/.../archives/arclength/arclength.ppt

What are we doing?

- In essence, we are subdividing an arc into infinitely many line segments and calculating the sum of the lengths of these line segments.
- For a demonstration, let’s visit the web.

Arc Length

- Note: Many of these integrals cannot be evaluated with techniques we know. We should use a calculator to find these integrals.

phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

Example Problem

- Compute the arc length of the graph of over [0,1].

Now comes the fun part…

- First, press the Math button and select choice 9:fnInt(
- Next, type the function, followed by X, the lower bound, and the upper bound.
- Press Enter and you get the decimal approximation of the integral!

Example

- Find the arc length of the portion of the curve on the interval [0,1]

phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

You try

- Find the arc length of the portion of the curve on the interval [0,1]

phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

Compiled by Mrs. King

Review:

- Find the volume of the solid created by rotating about the x-axis on the interval [0,2]

Picture from: http://math12.vln.dreamhosters.com/images/math12.vln.dreamhosters.com/2/2d/Basic_cubic_function_graph.gif

Surface Area of Solids of Revolution

- When we talk about the surface area of a solid of revolution, these solids only consist of what is being revolved.
- For example, if the solid was a can of soup, the surface area would only include the soup can label (not the top or bottom of the can)

phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

What are we doing?

- Instead of calculating the volume of the rotated surface, we are now going to calculate the surface area of the solid of revolution

Ex 2.5

- Find the surface area of the surface generated by revolving about the x-axis

phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

Closure

- Hand in: Find the surface area of the solid created by revolving about the x-axis

phs.prs.k12.nj.us/preyes/Calculus%205-4.ppt

Homework

- Page
- #

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