Place one of **the more recognizable forms**, such as a sphere, on the mat in front of you. Pick up and examine the solid by gently sliding **your hands** around it. "This is a spherical," explain to the youngster. Allow the youngster to have a turn repeating your activities and feeling **the geometric solid**. When finished, have him or her describe what they observed about the shape of the form.

Now that you know how to use these solids effectively, it's time to move on to another type of solid: linear.

To use a linear solid, start with a straightedge and compass. Have the child draw a line across the board. Explain that we can use this line to create other shapes by cutting along the edge of the line. Let him or her cut out a square, a rectangle, and a circle. Place **each shape** over the line on the board so that it fits exactly inside the corresponding shape cut from the solid. Help the child roll the solid in his or her mind's eye to see that it stays completely round or square regardless of which way it is rolled.

These are only some examples of how to use geometrical solids. You may want to expand on these ideas by having your youngster explore other types of solids, such as triangular, quadrilateral, pentagonal, etc. The important thing is that he or she has fun learning about these interesting objects that make up our world around us.

A sphere (from Greek sphairaâ€”sphaira, "globe, ball") is a three-dimensional geometrical entity that is the surface of a ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk"). These are also known as the radius and the center of the sphere, respectively. The term "sphere" can also be applied to other three-dimensional shapes, such as a cube or a dodecahedron; however, these are not generally considered solids for mathematical purposes.

Spheres are important in mathematics and science because many problems involving spheres can be solved by using spheres instead. For example, if you want to know how much milk would be needed to fill **a tank truck**, you could use the formula PV = nRT, where V is volume, n is the number of gallons, R is the radius of the truck bed, and T is the temperature in degrees Fahrenheit. This equation shows that the volume of milk required is proportional to the square of the radius of the truck bed. To keep the load equal, we need to increase the radius by a factor of 7/5 every time we add milk to the truck.

The problem with this approach is that it is extremely inefficient. It would require about a quart of milk for **each gallon** saved by **this method**. A better way to do this problem is to realize that the volume of milk required is constant, so we should just need to increase the amount of space we give it.

The forms of **solid objects** made of **certain materials** may be modified by squashing, bending, twisting, and stretching. The way these shapes are modified is called deformation. In general, the more rigid a material is, the less it can be deformed without breaking; therefore, the more rigid its natural state is. A very rigid material, like glass, cannot be deformed at all in **the natural state**.

All materials deform under pressure or force. Pressure from within, such as that produced by muscle tissue or blood cells, can cause a object to become thinner or longer. Pressure from without, such as that produced by hand or machine tools, can cause an object to become narrower or taller.

When a person squeezes a ball of soft rubber, for example, they are merely modifying its form. When viewed microscopically, **soft materials** such as rubber appear smooth because there are no visible edges or corners. But at a larger scale, such as that of a human being, these same materials have rough surfaces caused by compression. If a person were to push on a corner of this rubber ball, it would deform into a slightly flattened ellipse.

A sheet of paper can be bent without breaking if it is not too thick.

The following qualities characterize solids:

- Definite shape (rigid)
- Definite volume.
- Particles vibrate around fixed axes.

Solids, often known as three-dimensional things, have three dimensions: length, width, and height. Faces, edges, and vertices are all characteristics of solid forms. Learning about solid forms can benefit us in our daily lives because they are used in so many of our activities. As an example,

Solid Shapes | Cube |
---|---|

Faces | 6 |

Edges | 12 |

Vertices | 8 |

Three-dimensional things are solid forms. They are triangular in shape and have three dimensions: length, breadth, and height. They take up space in the cosmos because they are three-dimensional. Two-dimensional things are flat, and they only have two dimensions: length and breadth. Three-dimensional objects contain areas without dimension; for example, the surface of a ball is two-dimensional but its interior is three-dimensional.

Two-dimensional things can be shapes drawn with ink on paper, or they can be images stored on your computer's hard drive. When you view these images on **your screen**, you are viewing them visually but they are still just two-dimensional shapes. The term "solid" is used to describe shapes that have weight and take up space. A circle is an example of a two-dimensional solid shape while a cube is a three-dimensional solid shape.

You can describe any two- or three-dimensional shape as solid. These could be shapes made from clay, wood, metal, or even ice! You can also describe a four-sided object as solid since there are no openings inside it where something could go through. A pyramid is an example of a four-sided solid shape.

Shapes can also be described as hollow. Hollow shapes have spaces within them where things can go.

Geometric forms are most likely the most often utilized. They are the first thing that comes to mind. Circles, squares, triangles, pentagons, hexagons, and octagons are easily identified. They are so familiar to us since we began seeing and painting them as children. Geometric shapes are simple to draw yet provide the artist with a wide range of possibilities.

Beyond their aesthetic value, these figures have important implications for physics and mathematics. Scientists use **geometric shapes** to model physical systems -- such as atoms, molecules, crystals, and metals -- that are too complex to study completely analytically. Mathematicians use them to prove theorems or devise **new techniques**. In both cases, geometric thinking is essential in order to achieve one's goals.

There are many more types of figures than **just those** listed here. For example, there are convex and concave figures, orthographic and perspective views, empty and full figures. However, they are not as common as the ones mentioned above and thus do not get **much attention** in **school geometry classes**.

It is difficult to say which type of figure is the most common since they all appear frequently in nature and art. However, based on what we see around us, circles seem to be the most popular choice followed by squares. Other shapes are less common but none of them are rare.

Circle-shaped objects include rings, coins, and wheels.