How Big

We can finally calculate the volume of our theoretical mouthpiece! Again we use the Law of Sines to calculate the length of the cone, l. Here’s the original diagram so you don’t have to refer to another page:

cone_diagram

We know that angle c is equal to e’ or e both of which are 1.16 degrees, we know the side opposite angle c is r which is 0.660 cm, and we can calculate angle b since we know the value of e’. Side l is opposite angle b so we’re all set to do the arithmetic:

sideLcalc

That is one slender cone! 1.32 cm in diameter and 32.6 cm long, but what’s its volume? One more formula is needed:

volumeOfcone

and we can calculate the volume of our theoretical mouthpiece:

theoMouthpiecevol

While we may feel a certain amount of satisfaction with this, we still have to compare this volume to the volume of a real mouthpiece. Before we can do that there will be a short physical science review in: The Science Lesson

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s