A paragraph on circles and cylinders

In summary, the relationship between circles and cylinders is that a circle is the generating curve of a circular cylinder, obtained by moving a circle along a straight line path perpendicular to the plane of the circle. This can be demonstrated by defining and constructing a cylinder from a circle. Additionally, calculations can be performed to find the volume and surface area of a cylinder using the area of the circle. Furthermore, an infinite number of circles can be constructed from a given cylinder.
  • #1
murshid_islam
458
19

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.
 
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  • #2
Their relationship to pi?
 
  • #3
QuarkCharmer said:
Their relationship to pi?

Anything else?
.
 
  • #4
Well a circle has pi(r)^2, but the cylinder has a height measurement because it holds volume while a circle is 2d.
 
  • #5
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.
 
  • #6
Mark44 said:
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.


Mark44 said:
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.
.
 
  • #7
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'.
 
  • #8
epenguin said:
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. :confused:
.
 
  • #9
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).
 

Related to A paragraph on circles and cylinders

What is the definition of a circle?

A circle is a geometric shape that is defined as a closed curve where all points are equidistant from a fixed point called the center.

What are the properties of a circle?

The properties of a circle include having a constant radius, diameter, and circumference. The radius is the distance from the center to any point on the circle, the diameter is the distance across the circle passing through the center, and the circumference is the distance around the circle.

What is the formula for finding the circumference of a circle?

The formula for finding the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

What is the difference between a circle and a cylinder?

A circle is a two-dimensional shape, while a cylinder is a three-dimensional shape. A circle has only one curved surface, while a cylinder has two curved surfaces and two circular bases.

What are the applications of circles and cylinders in real life?

Circles and cylinders have many practical applications in everyday life, such as in architecture, engineering, and design. Cylinders are used in the construction of buildings and bridges, while circles are used in the design of wheels, gears, and other circular objects.

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