1.The height and radius are the same in both cylinders. Which cylinder has the greatest volume?2.This prism is cut by the plane shown. The plane is parallel to the base of the prism. What is the shape of the cross-section?
Accepted Solution
A:
Problem One This is one of those questions that you might think is silly until you try it for yourself or you read about it.
The thing you have to understand, which is not well stated, is that oblique cylinders have circles on the top and bottom. You guys (in the United States) still have pennies, don't you? Take 10 or twelve of them and make a stack where each penny sticks out 1/16 of an inch from the edge of the penny below it. I can't draw it I don't think (even my stick men look like someone who can't hold a pencil drew them), but maybe I can find a picture or you can.
Got it.
So the oblique cylinder has a circle on the top and bottom, just the way the pennies do when you stack them like the cylinder below. Then you can stack them like a soup can. Did anything change? No
The correct answer is (drum roll please) <<<<<<< They are the same volume.
Problem 2 Suppose you have a glass whose sides are straight up and down (a right cylinder with no top). You fill the glass with water. Stop a moment to consider this. Now magically you place a plain right through the middle of the glass.
Question: is there any difference between the shape of the plain at the top of the glass than that shape at the middle? (You should answer that they are the same shape -- a circle -- at both the top and middle of the glass).
If you caught on, you would have said that the shapes are the same in your question.