Cylinder - Shape, Properties, Formulas, Surface Area, Volume, Examples

Nov 30, 2022, 16:45 IST

A cylinder is the basic 3D geometric shapes with two parallel circular bases a certain distance apart. A curved surface connects two circular bases at a fixed distance from the center. The segment joining the center of the 2 circular bases is usually the axis of the cylinder. The distance between the 2 circular bases is known as the height of the cylinder. An LPG gas cylinder is an actual example of a cylinder.

Since a cylinder is a three-dimensional shape, it has two main properties, i.e., surface area and its volume. Total surface area of a cylinder is always equal to the sum of both the curved surface area of the cylinder and its area of ​​its two circular bases. The space occupied by the cylinder in three dimensions is called its volume.

Here we will learn about a cylinder's definition, formulas, and properties and solve some examples based on them. In addition to this image, we have the concepts of the sphere, cuboid, cone, cube, etc., which we learn in solid geometry.

Definition

In mathematics, a cylinder is a 3d solid that holds two parallel bases that is connected by the curved surface at a fixed distance. These bases are usually circular (like a circle), and the center of the two bases is joined by a line known as axis. The perpendicular distance between both the bases is the "h" height and the distance from the axis to the outer surface is the "r" radius of the cylinder.

Below is an image of a cylinder showing area and height.

Shape of Cylinder

A cylinder is a 3d shape consist of two parallel circular bases connected by the curved surface. A center of the circular bases overlaps each other to form the right cylinder. The line connecting the two centers is the axis that represents the height of the cylinder.

From the top view of the cylinder, it looks like a circle, and from the side view of the cylinder, it looks like a rectangle. Unlike cones, cubes, and cuboids, a cylinder has no vertices because the cylinder has a curved shape and has no straight lines. It has two circular faces.

Properties of Cylinder

Each shape has some properties that distinguish shape from another. That is why even cylinders have their own properties.

• The bases are always parallel and congruent.
• If the axis forms the right angle with the bases exactly above each other, then it is called "right cylinder."
• It is same to a prism because it has same cross-section everywhere.
• If the bases are not exactly across each other but to the sides, and the axis does not produce the right angle to the bases, it is called an "oblique cylinder."
• If the bases are circular, it is called a right circular cylinder.
• If the bases are elliptical, it is called an "elliptic cylinder."

Formulas

Below are the formulas of Cylinder:

1. Volume of the Cylinder, V = πr²h cubic units
2. Curved Surface Area = 2πrh square units
3. Total surface area, A = 2πr(r+h) square units

Solved Examples

Q1. Find the total surface area of the cylinder, whose radius is 4cm and height is 20cm.

Ans. We know,

Total surface area of a cylinder, A = 2πr(r+h) square units

Therefore, A = 2π × 4(4 + 20) = 2π × 4(24) = 2π × 96 = 192 × 3.14 = 602.88 cm²

Q2. Find the volume of a cylindrical shape water container that has a height of 8cm and diameter of 10cm?

Ans. Given,

Diameter of the container = 10cm

Thus, the radius of the container = 10/2 = 5cm

Height of the container = 8cm

As we know from the formula,

Volume of a cylinder = πr²h cubic units.

Therefore, volume of the given container, V = π × 64 × 8

V = π × 64 × 7 = (22/7) × 64 × 8 = 22 × 25

V = 1067.68 cm³

Also Read More About- Co-Prime Numbers, Successor and Predecessor

Frequently Asked Question (FAQs)

Q1. How many properties does a cylinder have?

Ans. Since the cylinder is a 3d shape, it has two major properties, i.e., surface area and volume.

Q2. What is the base of a cylinder?

Ans. The base area of the cylinder is usually the area of a circle, and therefore the base of the cylinder is a circle. A cylinder is a 3d solid figure which consists of the two circular bases connected with a curved face.

Q3. Are cylinders closed or open?

Ans. A cylinder is a closed solid with 2 parallel (generally circular) bases connected by a curved surface.

Q4. What is the value of a cylinder?

Ans. Volume of a cylinder is given by the formula, πr²h, where h is the height of the cylinder and r is the radius of the circular base.

Q5. Who invented cylinder formula?

Ans. The famous mathematician and the inventor in ancient Greece "Archimedes", (born c. 287 bce, Syracuse, Sicily [Italy]—died 212/211 bce, Syracuse. He is important for his discovery of the relation between the surface and the volume of a sphere and its circumscribing cylinder.