Have you ever wondered what to call a 3D figure made from an elongated circle? This unique shape is actually known as a “torus,” and it has a wide range of applications in fields such as mathematics, engineering, and even art.
The torus is a fascinating shape that is formed by taking a circle and rotating it around an axis that is perpendicular to the plane of the circle. The resulting 3D figure has a distinct shape that resembles that of a donut, with a hole in the center. While it may seem like a simple shape, the torus has a number of interesting properties that make it useful in a variety of different contexts.
Whether you’re a mathematician looking to explore the properties of different shapes, an engineer designing a new piece of machinery, or an artist looking for inspiration, the torus is a shape that is definitely worth exploring. In the following article, we’ll take a closer look at what makes the torus so unique, and explore some of the many ways in which it is used in different fields.
Defining the 3D Figure
What is an Elongated Circle?
An elongated circle is a shape that is created by stretching a circle along one of its axes. This shape is also known as an ellipse or an oval. When viewed from different angles, an elongated circle can appear to be a variety of different shapes, including a rectangle, a square, or a parallelogram.
How is a 3D Figure Made from an Elongated Circle?
To create a 3D figure from an elongated circle, the circle is first stretched along one of its axes to create an ellipse. The ellipse is then rotated around its minor axis to create a 3D shape that resembles an elongated cylinder. This shape is known as a cylindrical prism or a cylinder.
The cylinder can then be further modified to create a variety of different 3D shapes. For example, if the top and bottom of the cylinder are capped with circles, the result is a shape known as a cylinder with circular bases, or a cylinder for short. If the top and bottom of the cylinder are capped with ellipses, the result is a shape known as a cylinder with elliptical bases.
In conclusion, an elongated circle is a shape that is created by stretching a circle along one of its axes. When rotated around its minor axis, an elongated circle can be used to create a variety of different 3D shapes, including cylindrical prisms, cylinders, and more.
Types of 3D Figures Made from Elongated Circles
When it comes to 3D figures made from elongated circles, there are three main types: cylinders, cones, and capsules. Each of these figures has its own unique characteristics and uses.
Cylinders
A cylinder is a 3D figure that has two parallel circular bases connected by a curved surface. The height of the cylinder is the distance between the two bases. Cylinders are commonly used in everyday objects such as cans, pipes, and bottles. They are also used in engineering and architecture for designing structures such as bridges and buildings.
Cylinders can be classified into two types: right cylinders and oblique cylinders. A right cylinder has its axis perpendicular to its bases, while an oblique cylinder has its axis at an angle to its bases.
Cones
A cone is a 3D figure that has a circular base and a curved surface that tapers to a point called the apex. The height of the cone is the distance from the apex to the base. Cones are commonly used in everyday objects such as traffic cones and ice cream cones. They are also used in engineering and architecture for designing structures such as chimneys and towers.
Cones can be classified into two types: right cones and oblique cones. A right cone has its apex directly above the center of its base, while an oblique cone has its apex off-center from the base.
Capsules
A capsule is a 3D figure that has two circular bases connected by a cylindrical surface. The height of the capsule is the distance between the centers of the two bases. Capsules are commonly used in everyday objects such as pills and capsules for medication. They are also used in engineering and architecture for designing structures such as domes and arches.
Capsules can be classified into two types: prolate capsules and oblate capsules. A prolate capsule has a longer cylindrical surface than its diameter, while an oblate capsule has a shorter cylindrical surface than its diameter.
In conclusion, 3D figures made from elongated circles come in a variety of shapes and sizes, each with its own unique characteristics and uses. Whether you are designing a building or taking medication, understanding these figures can help you make informed decisions and create effective solutions.
Properties of 3D Figures Made from Elongated Circles
Volume and Surface Area
3D figures made from elongated circles are commonly known as cylinders. A cylinder has two circular bases that are parallel and congruent. The distance between the two bases is the height of the cylinder. The volume of a cylinder can be calculated by multiplying the area of the base by the height. The formula for the volume of a cylinder is:
V = πr²h
where V is the volume, r is the radius of the base, and h is the height of the cylinder.
The surface area of a cylinder can be calculated by adding the area of the two bases and the lateral area. The formula for the surface area of a cylinder is:
A = 2πr² + 2πrh
where A is the surface area, r is the radius of the base, and h is the height of the cylinder.
Symmetry
A cylinder has rotational symmetry around its central axis. This means that if you rotate the cylinder around its central axis, it will look the same at every angle. The two circular bases are congruent, and the lateral area is a rectangle that is perpendicular to the bases. The lateral area is also symmetrical, as it is the same shape and size on both sides of the cylinder.
Proportionality
The volume and surface area of a cylinder are directly proportional to the radius and height of the cylinder. This means that if you double the radius or height of a cylinder, the volume and surface area will also double. Similarly, if you halve the radius or height of a cylinder, the volume and surface area will also be halved.
In summary, 3D figures made from elongated circles, or cylinders, have unique properties that make them useful in various applications. They have a simple formula for calculating their volume and surface area, symmetry around their central axis, and proportionality between their dimensions and volume/surface area.
Real-World Applications
Architecture
In architecture, 3D figures made from elongated circles, also known as ellipsoids, are commonly used to design and visualize buildings and structures. Ellipsoids can be used to create domes, arches, and other curved surfaces, making them a valuable tool for architects to create unique and aesthetically pleasing designs.
Ellipsoids are also used in structural analysis to determine the strength and stability of buildings. By creating a 3D model of a building using ellipsoids, engineers can simulate different loads and forces to ensure the structure can withstand them.
Engineering
In engineering, ellipsoids are used to create models of complex mechanical parts and systems. These models can be used to test the performance of the parts and systems before they are manufactured, saving time and money in the development process.
Ellipsoids are also used in fluid dynamics to simulate the flow of liquids and gases in pipes and other structures. By creating a 3D model of the structure using ellipsoids, engineers can predict how fluids will flow and identify areas of turbulence or pressure drop.
Art and Design
In art and design, ellipsoids are used to create sculptures and other 3D art pieces. The unique shape of an ellipsoid allows artists to create dynamic and interesting forms that are not possible with traditional geometric shapes.
Ellipsoids are also used in product design to create ergonomic and aesthetically pleasing shapes for products such as cars, furniture, and electronics. By using ellipsoids, designers can create products that are both functional and visually appealing.
Overall, the use of ellipsoids in various fields demonstrates their versatility and usefulness in creating 3D models and designs.
