Cylinder

Introduction

The cylinder obtained by rotating a line segment about a fixed line that it is parallel to is a cylinder of revolution. In our everyday lives, we are familiar with several cylindrical objects. Traditional definitions of a cylinder or cylindrical structure include a three-dimensional solid with a prism-like form and a circle at the base, as pencil, road roller, and pipes are some basic examples of cylinders.

One of the most fundamental curvilinear geometric forms is this one. This conventional viewpoint is still helpful in resolving simple geometric issues. A cylindrical surface, however, is viewed from a complex mathematical perspective as an infinitely curved surface. Today, many current fields of geometry and topology follow this notion. We shall discuss the features, varieties, and formulas associated with cylindrical constructions in this article.

Today we will discuss the properties of the cylindrical body, the parameters used in the shape, and deal with some problems.

Cylinders

It is made of parallel circular discs; we can say that a large number of circular discs will make a cylinder. If we join all the centres of the circular disc, A line segment joining the axis will be the height of the cylinder.

• The cylinder seems to be a circle from the top.

• The front view of the cylinder looks like a rectangle. It has curved lines, not straight as cube and cuboid

Types of cylinders

• Elliptical cylinder − An elliptical cylindrical structure is a cylinder with elliptical bases.

• Right circular cylinder − By rotating the rectangle around one of its sides as an axis, an object known as a right circular cylinder is created. The cylinder is referred to as a right circular cylinder if the axis (one of the rectangle's sides) is perpendicular to the radius (r). The height (h) of a cylinder is the distance between its round faces at its top and bottom, which are parallel to one another.

• Oblique cylinder − An oblique cylinder is one in which the circular faces are sideways rather than over one another, and the axis creates an angle other than a straight angle to the bases.

• Hollow cylinder − A hollow cylinder is a cylindrical construction that has a difference between its outer and inner surface diameters and is empty from the inside. Since the inner and outer diameters are variable, they can have various inner and outer lateral surface areas.

Formulas of cylinders

In three-dimensional geometry, the entire area filled by a cylinder is known as its area. The total surface area of two circular bases plus the lateral surface area makes up the area of a cylinder. Between two circular bases, there is a curved or lateral surface. When the curved surface is opened, a rectangular figure is represented. Height, radius, axis, side, and base are the many variables used to calculate the cylinder area. The cylinder's radius is equivalent to the distance between its two circular sides. The perpendicular distance between two circular sides is referred to as the cylinder's height, and its radius can be written as (r). The cylinder's height is specified as (h)

A cylindrical structure's surface area may be divided into two categories.

• Curved surface area (CSA)

• Total surface area (TSA)

Curved surface area or lateral surface area

Lateral surface area is another name for curved surface area. The area of a curved surface is the area of a cylindrical structure except for the area of its circular base.

In general, square units like centimeter square, meter square, etc. are used to measure area.

A rectangular form may be seen if the cylinder's curved surface area is opened.

Two circular edges on the curved surface area may match the circle's diameter in size.

The circle's circumference may be calculated using the formula 2r.

Therefore, the rectangle's length (after opening the curved surface) is 2r, and its width is (h). As a result, the area of the curved surface is 2Πrh.

So, the formula is given by

$$\mathrm{The\: curved\: surface\: area\: of\: the\: cylinder\: = 2Πrh\: square\: units.}$$

Total surface area

The total surface area of the cylinder is the sum of the area of the two circles and the curved or lateral surface area and it is given by

Total surface area = area of two circles + curved surface area

$$\mathrm{=2×Πr^2+2Πrh }$$

$$\mathrm{ =2Πr(r+h)\: square\: unit}$$

Volume

Every solid or three-dimensional shape has a volume that takes up some space. The area that the cylinder occupies in any three-dimensional plane is its volume. The capacity of a cylinder indicates how much water might be contained within.

$$\mathrm{Volume\: of\: cylinder\: = Πr^2 h\: cube\: units}$$

Solved examples

1)What is the radius of the cylinder if the height of the cylinder is 12cm, and the volume of the cylinder is to be 8478cm³?

Answer:

Given that, the height of the cylinder (h) =12cm

Volume of the cylinder (v)=8478cm³

as we know,

volume of cylinder(v) = Πr² h

$$\mathrm{8478 = 3.14×r^2×12}$$

$$\mathrm{8478 = 37.68×r^2}$$

$$\mathrm{225 = r^2}$$

Hence, r = 15cm

So the radius of the cylinder is 15cm.

2)What is the volume of the cylindrical shape of a water tank if the diameter and height of the tank are 30cm and 40cm, respectively?

Answer:

Given, height of the cylindrical water tank (h) = 40cm

Diameter of the cylindrical tank (d) = 30cm

so, the radius of the cylindrical tank (r)= 30/2 =15cm

as we know,

the volume of the cylinder = Πr² h

$$\mathrm{= 3.14×15×15×40}$$

$$\mathrm{= 28260cm^3}$$

3) What is the total surface area of a cylinder whose radius and height are 7cm and 20cm, respectively?

Answer:

Given,

Radius of the cylinder(r) = 7cm

Height of the cylinder(h) = 20cm

as we know,

The total surface area of the cylinder = 2Πr(r+h)

$$\mathrm{= 2×3.14×7×(20 +7)}$$

$$\mathrm{ = 1,186.92cm^2}$$

So, the surface area of the cylinder is 1,186.92cm².

Conclusion

A cylindrical construction has zero vertices, two edges, one curved surface, and two bases. It has two bases, like a prism. Their forms may be divided into four categories: hollow cylindrical structures, elliptical cylinders, right circular cylinders, and cylindrical structures. A cylindrical construction has two parallel bases, and the distance between the two bases is referred to as its altitude or height.

• The Curved surface area of the cylinder = 2Πrh square units.

• The total surface area of the cylinder = area of two circles + curved surface area

  $$\mathrm{= 2×Πr^2+2Πrh}$$

  $$\mathrm{= 2Πr(r+h) \: square\: unit}$$

• The volume of the cylinder = Πr² h cube units

FAQs

1. A Cylinder Has How Many Faces?

In a cylinder, there are two flat circular sides and one curved surface. Thus, it has three faces altogether.

2. Does the cylinder have vertices?

Two parallel, round sides that make up a cylinder have the same form. However, because of its curvature, it lacks any vertices.

3. What other cylinder kinds are there?

Right circular cylinders, oblique cylinders, elliptical cylinders, and hollow cylinders are the four different forms of cylinders.

4. What makes a cylinder a 3D shape?

A cylinder is a three-dimensional form that has two parallel, round sides on either end. One side that curves. No vertices or edges.