A paragraph on circles and cylinders

[murshid_islam]

Homework Statement

My niece has to write a paragraph on circles and cylinders. This is the exact question: "How are circles and cylinders related? Write a paragraph to explain what you learned about circles and cylinders."

Homework Equations

The Attempt at a Solution

I am thinking about comparing
a) the area of a circle and volume of a cylinder
b) the circumference of a circle and surface area of a cylinder

Any ideas about what else can be included in the paragraph? Thanks in advance.

 

[QuarkCharmer]

Their relationship to pi?

 

[murshid_islam]

Their relationship to pi?

Anything else?
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[DeathCrawls]

Well a circle has pi(r)^2, but the cylinder has a height measurement because it holds volume while a circle is 2d.

 

[Mark44]

Unless we're talking about circular cylinders, I'm not sure that I see any relationship at all. For example, the graph of y = x² in three-dimensional space is one type of cylinder (parabolic) that has a sort of trough shape.

If we limit the discussion to circular cylinders, a circle is the generating curve of this type of cylinder in which a right circular cylinder is obtained by moving a circle along a straight line path perpendicular to the plane of the circle.

 

[murshid_islam]

Unless we're talking about circular cylinders, I'm not sure that I see any relationship at all. For example, the graph of y = x² in three-dimensional space is one type of cylinder (parabolic) that has a sort of trough shape.

We are talking about circular cylinders.

If we limit the discussion to circular cylinders, a circle is the generating curve of this type of cylinder in which a right circular cylinder is obtained by moving a circle along a straight line path perpendicular to the plane of the circle.

Already mentioned that. But thanks anyway.
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[epenguin]

You could define or state a construction of a cylinder starting from a circle. What about the inverse of that? You may have at some time been supplied with some high-falutin waffle that you are now required to bring up, it might well include the phrase 'the set of'.

 

[murshid_islam]

You could define or state a construction of a cylinder starting from a circle. What about the inverse of that? You may have at some time been supplied with some high-falutin waffle that you are now required to bring up, it might well include the phrase 'the set of'.

I didn't understand what you meant.
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[epenguin]

Never mind the last sentence. Starting from a circle surely she can give a definition and a construction of a cylinder?

Then maybe an elementary calculation or two. For instance from the area of the circle deduce the volume of a finite cylinder? The surface area of the cylinder? (General formulae in terms of radius r and height h.) Given a cylinder how many circles can you construct? (an infinite number).