Cylinder
The word "cylinder" is derived from the Greek word "Kylindros," meaning "roll" or "roller." A cylinder is a three-dimensional figure that is made up of a curved surface, a circular top, and a circular bottom. It is one of the most basic curvilinear geometric shapes that has both mathematical and real-world applications. Toilet paper rolls, cold drink cans, and pipes are a few of the basic examples of the cylinder shape in real-life situations. In this blog, we will explore different types of cylinders and essential formulas like surface area (CSA and TSA of cylinder) and volume of a cylinder.
1.0Key Properties of a Cylinder
Every geometrical shape has its own unique characteristics, and a cylinder is no different. Let’s look at some of the key properties of a cylinder:
- Every cylinder is made up of a curved surface and two flat faces, which are identical.
- A cylinder does not have any verticals like a cone, cube, or cuboid.
- The two circular bases are always congruent and parallel.
- The size of a cylinder is determined by the height and radius of the base.
- A cylinder has the same base and the same top, whether it is circular or elliptical.
2.0Types of Cylinders
Cylinders come in different types based on the cylindrical shapes and orientation. There are five types of cylinders, which are right circular cylinders, half-cylinders, elliptical cylinders, hollow cylinders, and horizontal cylinders. Refer to the below table to understand the different types of cylinders in detail.
3.0Surface Area of a Cylinder (CSA and TSA of Cylinder)
The surface area of an object refers to the total area occupied by the said object. The cylinder is a common three-dimensional geometric shape. Because of its three-dimensional nature, one needs to calculate the curved surface area and the total surface area, known as the CSA and TSA of Cylinder.
Curved Surface Area (CSA) of a Cylinder
The curved surface area refers to the area of only the curved surface, leaving the circular top and the base. If the height of a cylinder is seen as “h” and the base radius as "r,” then the curved surface area of a cylinder would be:
C.S.A= 2πrh
Example: Find the curved surface area of a cylinder with a radius of 14 cm and a height of 21 cm.
Solution:
CSA=2πrh
Now the value of r=14 cm (radius), h=21 cm (height), and π≈3.1416
Now, substituting the values:
CSA = 2 × 3.1416 × 14 × 21
CSA =2 × 3.1416 × 294
CSA = 1847.52 cm²
So, the curved surface area of the cylinder is 1847.52 cm².
Total Surface Area (TSA) of a Cylinder
The total surface area of a cylinder includes the area of the surface as well as the two circular bases. If the cylinder has the base radius "r” and the height is denoted by “h,” then the total surface area of a cylinder is the sum of the curved areas and the circular areas of the cylinder.
TSA = 2πr(r + h)
Example: Find the total surface area of a cylinder having a radius equal to 5 cm & height 8 cm.
Solution:
The total surface area (abbreviated as TSA) of a cylinder may be calculated using the formula TSA = 2πr(r + h).
By substituting the values of radius (r) = 5, height (h) = 8, we get:
TSA = 2πr2+2πrh = 2πr(r+h) = 2 × 3.14 × 5(5 + 8) = 408.41 cm².
4.0Volume of a Cylinder
The volume of a cylinder refers to the amount of space the cylinder can hold. To calculate the volume of a solid cylinder, one needs to multiply the base area of the cylinder by its height.
Volume: π r² h
Example: A cylinder has a radius equal to 50 cm and a height equal to 100 cm. How to find the volume of a cylinder?
Solution:
As we know, the volume of a cylinder is given by the formula – π r2 h, where
r is its radius = 50 cm and
h is the height = 100cm.
Therefore, putting the values we get,
V = π r² h
V = 3.14 x 502 x 100
V = 785,000 cm³
5.0Conclusion
By understanding the cylinder and its mathematical applications, you can apply them in real-world situations and significantly benefit from it. Students are advised to practise questions based on CSA and TSA of Cylinder as well as how to calculate the Volume of a Cylinder to ace their examinations.
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