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Cylinder Definition in Maths, Surface Area and Volume of a Cylinder

 

A cylinder is a special type of 3D figure distinct from other regular-shaped three-dimensional objects. It is a curved figure, which means that it encloses the concept of radius and ‘pi’ in it. A cylinder has two flat bases, one at the top and the other at the bottom of the object. They are both parallel to each other and are connected using the curved surface. The circular bases' centers imbricate or lie over each other to form a right cylinder. The axis is the line segment that connects the two centers and represents the height of the cylinder. The top view of the cylinder resembles a circle, while the side view resembles a rectangle. A cylinder, unlike a cone, cube, or cuboid, lacks vertices due to its curved form and lack of straight lines. It features two concentric circles on its face. Some of the basic properties of a right circular cylinder are mentioned below:

  • The circular bases are similar or congruent to each other. If they were of different shapes, the shape would change from being cylindrical.
  • If the center of the circle on the top perfectly coincides with the center of the circle on the bottom, it forms a right circular cylinder, with and height and base being perpendicular to each other. However, there are some cylinders where the height is a little slanted. Such cylinders are known as Oblique cylinders.
  • For a right circular cylinder, the bases should also be perfectly circular. In case the bases are elliptical, then the cylinder is known as an elliptical cylinder.
  • The area of cross-section throughout a cylindrical shape is equal, making it identical to a prism.

The water bottles, toilet paper rolls, pickle jars, LPG cylinders, etc., are real-life examples of cylindrical objects. Let us learn the important parameters of a cylinder that are the surface area and volume.

Surface Area

There exist two surface areas for a cylinder. The surface area of a cylinder is the amount of region swept by the cylinder in the 3D space. The cylinder doesn’t have many faces, but it consists of a curved surface. The total area covered by this curved surface is known as the curved surface area (CSA) and is formulated as: CSA = 2 x pi x s x d or 2πsd The total surface area of a cylinder is conceptualized as a curved surface area plus the area of the two bases with a radius equal to 's' and height of the cylinder as 'd'. Therefore,

Therefore, TSA = CSA + 2 * (area of circles)

= 2πsh + 2 * (πs2)

= 2πs (d + s) 
 

Volume

The volume of a cylinder is defined as the amount of space present inside the cylinder. The amount (liters) of water that can be contained in a cylinder is known as its volume. It is calculated utilizing the formula: Volume of a cylinder = pi x s2 x d. Where 's' is the radius of the circular bases and d is the height or depth of the cylinder. It is measured in cubic units (m or cm)

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