Cylinder facts for kids
A cylinder is a basic three-dimensional shape that is curved. Think of it like a can of soda or a toilet paper roll. It has two flat, circular ends that are parallel to each other, and a curved side connecting them.
The word "cylinder" can mean two things:
- The surface of the shape, like the outside of a can.
- The solid shape itself, including everything inside.
People have known how to figure out the space inside a cylinder (its volume) and the area of its surface for a very long time!
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What is a Common Cylinder?
When most people talk about a cylinder, they usually mean a right circular cylinder. This is a cylinder where the curved side stands straight up, making a perfect right angle with the flat circular ends.
Imagine a cylinder with a circular base.
- The distance from the center of the circle to its edge is called the radius (we use the letter r).
- The distance between the two circular ends is called the height (we use the letter h).
How to Find the Volume
The volume of a cylinder tells you how much space it takes up. You can find it using this formula:
- V = πr2h
Here, V stands for volume, π (pi) is a special number (about 3.14159), r is the radius, and h is the height.
How to Find the Surface Area
The surface area is the total area of all the surfaces of the cylinder. This includes the top circle, the bottom circle, and the curved side.
To find the total surface area:
- Area of the top circle: πr2
- Area of the bottom circle: πr2
- Area of the curved side: 2πrh
So, the total surface area (A) is:
- A = 2πr2 + 2πrh
This can also be written as:
- A = 2πr(r + h)
If you only want the area of the curved side (without the top and bottom), the formula is:
- A = 2πrh
Did you know? For a cylinder to hold the most volume for its surface area, or have the smallest surface area for a certain volume, its height (h) should be exactly twice its radius (h = 2r). This means it would fit perfectly inside a cube!
Cylinder Slices
Imagine slicing a cylinder with a flat plane, like cutting a loaf of bread. The shape you get from the cut is called a cylindric section.
Here are some ways you can slice a right circular cylinder:
- If you slice it perfectly straight down, touching only one side, you get a single straight line.
- If you slice it straight down but through the middle, you get two parallel lines.
- If you slice it straight across, parallel to the circular ends, you get a circle.
- If you slice it at an angle, you get an ellipse (an oval shape).
Other Kinds of Cylinders
Not all cylinders are perfectly circular like a can. There are other types too!
Elliptic Cylinder
An elliptic cylinder is like a circular cylinder, but its base is an ellipse (an oval) instead of a perfect circle. Imagine squishing a circular can from the sides – that's an elliptic cylinder.
Oblique Cylinder
An oblique cylinder is one where the top and bottom circles are not directly above each other. The curved side is slanted, making the cylinder lean over, like the Leaning Tower of Pisa.
More Unusual Cylinders
There are also other types of cylinders that are more complex and are studied in advanced math:
- Hyperbolic cylinder: This cylinder has a cross-section that looks like a hyperbola (two curves that mirror each other).
- Parabolic cylinder: This cylinder has a cross-section that looks like a parabola (a U-shaped curve).
Cylinders in Projective Geometry
In a special type of math called projective geometry, a cylinder can be thought of as a cone whose tip (called the apex) is so far away that it's considered to be at "infinity." This idea helps mathematicians understand different shapes in new ways.
Images for kids
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Cylindric sections of a right circular cylinder
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In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.
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The Tycho Brahe Planetarium building in Copenhagen is shaped like a truncated cylinder.
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See also
In Spanish: Cilindro para niños
