A cylinder is the most common geometric shape, appearing in everything from coffee mugs to gas tanks and fuel containers.
The most common shape is the cylinder, which is derived from the Greek word ‘kulindros’, which means tumbler.
The capacity of these often-used shapes will be discussed in the following chapter. In this blog, we are going to find the surface area and volume of cylinder. Let us begin:
What is a Cylinder?
A cylinder is a closed solid object with two parallel bases that are often round in shape and two parallel sides that join them. A rectangle with circular bases can also be characterized as a cylinder.
These circular bases are invariably congruent and parallel to each other. When a cylinder is unrolled, it takes on the shape of a rectangle. A cylinder is formed when the base and sides are joined together.
The axis that connects the two circular bases. Height (h) provided is the only perpendicular distance between the two bases. Each base has a respective radius (r). The measurement provided of the height and radius help us obtain the volume and surface area of cylinder.
Curved Surface Area:
We must first wrap a cylindrical can with a sheet of paper in order to calculate the curved surface of this geometrical shape. The paper should be taped together in such a way that it fits snugly inside the cylindrical can.
From the above discussion, we can know, the length of the cylinder = the circumference of the base that is 2πr. The breadth of the rectangle = Height of the cylindrical can be expressed as h.
Now, since the rectangular paper was used to wrap the Can firmly, we know that area of a rectangle is equal to the area of the curved surface of the Cylindrical can = l × b = 2πr × h
The Curved Surface Area of the Cylinder, is, therefore, 2πrh
A cylindrical shape is made up of two circular bases and a rectangle-like form that connects the two bases, as we already know. As a result, the area of the two bases and the curved surface area must be included in the overall surface area of this geometrical form.
As a result, total surface area = Area of base 1 + Area of base 2 + Curved surface area = Curved surface area = πr2 +πr2 + 2πrh = 2πr2 + 2πrh = 2πr (r+h). The Surface Area of a Cylinder = 2πr (r+h)
Volume of Cylinder
As previously stated, a cylindrical shape is made up of rectangles of the same size. We can make a cylinder with the help of two circular bases. Now, in order to calculate the volume of this form, we use the cuboid, a 3D equivalent of the rectangle.
We can calculate the volume of any cylindrically shaped container using the volume of a cuboid formula. We already know that the volume of a cuboid is equal to the product of a rectangle’s area and its height; l b h.
A 3D cylindrical container is in the same scenario. To calculate the volume, multiply the base area by the height. As a result, the volume of a cylindrical container is equal to the area of the circular base multiplied by the height, which equals πr2 × h.
As a result, the Volume of a Cylinder = πr2 h. You can learn more about such concepts with Cuemath. Cuemath is an online learning platform that enables you to understand concepts in detail thus providing students an in-depth understanding of the topic.
Types of Cylinders:
There are mainly two types of cylinders in geometry according to their properties and composition.
- Right Cylinder: Whenever the two bases of the cylinder are overlapping over each other in the exact position and the axis is at the right angle to the base, such a cylinder is recognized as a right cylinder.
- Oblique Cylinder: Whenever any one of the bases of the cylinder is sideways and the axis is not a right angle to the base, then it is recognized as an oblique cylinder.