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:

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:

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:

and we can calculate the volume of our theoretical mouthpiece:

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

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