Expert: Scotto - 9/14/2010

Question
QUESTION: in the figure is shown a block of wood in the form of a right prism whose bases are right triangles. a cylindrical auger hole of diameter 2 in. is bored through the block. if the elements of the cylindrical hole are perpendicular to the face ABEF and if the lateral surface of the cylindrical hole is tangent to face ABCD, find the volume removed

taken from solid mensuration book, thanks for the time, and only scotto seems to be the only guy who can solve this

ANSWER: The length of the hole at the base is 8".
The length of the hole 2" up is 8" - 4/3 of the distance up.
The distance up is the diameter, and that is 2".
This makes the cyllinder 16/3".
When the two lengths are averaged, they will give the length to be used.

So, determine the are of a circle width a diameter of 2" (so the radius is 1 and the area is pi) and multiply this by the average length since the amount sticking over the average length is the same as the amount missing.


---------- FOLLOW-UP ----------

QUESTION: ah follow up though. average length would be? is a cylindrical auger  a T shaped cylinder or something. what did u mean the length of the hole up? thanks for your time :)  

Answer
Find the height on the block of the center of the cyllinder.

Find the length at that height.

Picture taking the amount that is over this length below the center and pasting it backwards up above.  

This gives a perfect cyllinder with the length at the center.

To find the exact length, take the equation of the vertical line and find where the endpoint should be 1 inch above and below the center.

For further assistance, I need to see the problem again.
I tried to view it, but couldn't. :(