Find Number of Feet

[harpazo]

Section R.3
Geometry Essentials
Michael Sullivan
Textbook: College Algebra Edition 9

How many feet does a wheel with a diameter of 16 inches travel after 4 revolutions?

Solution:

I know that C = pi•d.

C = pi•16

C = 3.14 • 16

C = 50.24 inches

After 4 revolutions, I must calculate 4•C.

So, 4(50.24) = 200.96 inches.

How do I convert 200.96 inches to feet?

Stuck here....

Note: We are now in R.3 in the Sullivan textbook.

 

[Otis]

… How do I convert 200.96 inches to feet? …

\[\frac{200.96 \text{ in}}{1} × \frac{\text{1 ft}}{\text{12 in}}\]

? If Sullivan instructed you to use 3.14 for pi, then 200.96 is okay. Otherwise, approximating pi as 3.1415 gives a better result.

\(\;\)

 

[harpazo]

\[\frac{200.96 \text{ in}}{1} × \frac{\text{1 ft}}{\text{12 in}}\]

? If Sullivan instructed you to use 3.14 for pi, then 200.96 is okay. Otherwise, approximating pi as 3.1415 gives a better result.

\(\;\)

Ok. Sullivan did not say to use pi or 3.14.
In that case, using 3.1415 leads to

C = pi•16

C = 3.1415 • 16

C = 50.264 inches

Then 4 • 50.264 inches = 201.056

 

[MarkFL]

If not instructed to use a decimal approximation for \(\pi\), then I would give my result as a multiple of \(\pi\).

 

[harpazo]

If not instructed to use a decimal approximation for \(\pi\), then I would give my result as a multiple of \(\pi\).

C = pi•16

C = 16pi

Then 4 • 16pi = 64pi.

Yes?

 

[Steven G]

Yes, but what are the units? Then convert to feet.

 

[harpazo]

Yes, but what are the units? Then convert to feet.

I asked my friend who is at home to text me the answer. He said that Sullivan requested the answer in terms of pi.

 

[Steven G]

C=16pi inches. Now to change the way it looks (you want ft not inches) you need to multiply by 1. That is a basic rule! To change the way something looks, just multiply by 1. Say this to yourself 1000 times.
16pi inches = (16pi inches) (1) = (16pi inches)(1 ft/12 in) = (4/3)pi ft

 

[harpazo]

C=16pi inches. Now to change the way it looks (you want ft not inches) you need to multiply by 1. That is a basic rule! To change the way something looks, just multiply by 1. Say this to yourself 1000 times.
16pi inches = (16pi inches) (1) = (16pi inches)(1 ft/12 in) = (4/3)pi ft

Interestingly stated.

 

[MarkFL]

Interestingly stated.

That is essentially the same thing my dad taught me when I was a kid and what I've tried to show you.

 

[harpazo]

That is essentially the same thing my dad taught me when I was a kid and what I've tried to show you.

You have not failed, Mark. I have learned a great deal of math with your help.