Area of Hollow Cylinder: Total & Lateral Surface Area with Formula

A cylinder is a three-dimensional solid object that has two bases that are both exactly circular and are connected by a curved surface that is offset from the centre. Batteries, water bottles, gas cylinders, pipes, etc. are examples of cylinders in daily life. A hollow cylinder's area can either refer to the cylinder's flat top surface or its curved top surface.

Cylinder

Geometry includes dimensions, sizes, angles, shapes, and many other concepts that we encounter every day. In plane geometry, common shapes like squares, rectangles, circles, triangles, and others are flat and two-dimensional. The term "solid shape" in solid geometry refers to shapes that appear to have a three-dimensional structure, such as a sphere, cube, cuboid, cone, Cylinder etc.

A cylinder is a 3D solid shape made up of two parallel bases that are identical to one another and are connected by a curved surface. These bases resemble discs in shape. The axis of the cylinder shape is created by drawing a line through the centre or connecting the centres of two circular bases. Height, abbreviated as "h," is the angle between the two bases. The radius of the cylinder abbreviated as "r," is the distance between the centres of the two circular bases. The cylinder is composed of two circles and a rectangle. Let's look at the image below.

Type Of Cylinder

Majorly there are four different types of cylinders in geometry and they are:

• Right Circular Cylinder: Right circular cylinder is the cylinder in which the axis of the two parallel bases is perpendicular to the centre of the base.

• Oblique Cylinder: An oblique cylinder is a cylinder in which one side leans over the base and the sides are not perpendicular to the centre of the base. One of the real-life examples of oblique cylinders is The Leaning Tower of Pisa.

• Elliptic Cylinder: An Elliptic Cylinder is a cylinder whose base is in the form of an ellipse.

• Right Circular Hollow Cylinder: This is also known as Cylindrical Shell, this Cylinder consists of two right circular cylinders bounded one inside the other. The point of the axis is the same and is perpendicular to the central base. It is different from the other cylinder because it is hollow, i.e. there is some void present inside it.

Hollow Cylinder

A hollow cylinder can be defined as a type of cylinder which is vacant or empty from the inside. Or A cylinder that has some difference between the internal and external radius and is empty on the inside is said to be hollow. In other words, it is a cylindrical shape with some thickness at the edges and no interior. Some of real-life examples of hollow cylinders are, pipes, straws, pen-pencil holders, food or drink can, etc. An image of a hollow cylinder is given below.

Volume Of A Hollow Cylinder

A three-dimensional object with a circular base, the cylinder. A cylinder can be visualized as a collection of stacked circular discs. While a hollow cylinder is characterized as having a difference between the internal and external radii and being empty on the inside.

When the hollow cylinder's outer and inner radii are known, its volume can be calculated as follows:

Volume of the hollow cylinder, V = π (R2 - r2)h units3

Here,

R = outer radius of the given hollow cylinder.

r = inner radius of the given hollow cylinder.

h = height of the given hollow cylinder.

Area Of A Hollow Cylinder

The area of a hollow cylinder in two dimensions is the surface area covered by its walls. This 2D property of any geometric figure, whether 2D or 3D, exists. There are many types of surface area depending on the part of the hollow cylinder we examine.

Lateral Surface Area Of A Hollow Cylinder

The lateral surface area of the hollow cylinder is constituted of the inner surface area and the outer surface area together. It is also known as the curved surface area of the hollow cylinder because only the curved surfaces are considered.

Let the Outer radius of the hollow cylinder is ‘R’ and the inner radius of the hollow cylinder be ‘r’

Then, the lateral surface area of the hollow cylinder is :

Total Surface Area Of A Hollow Cylinder

The total surface area of a hollow cylinder is the total area that a hollow cylinder is capable of having. In other words, the total surface area of the hollow cylinder is obtained by adding the area of the curved surface to the areas of the two bases.

Given that the bases, in this case, are merely a ring, we can use the cross-section calculation to get their area. However, we should be aware that since a hollow cylinder has two bases, we must double-add this cross-sectional area.

Let the Outer radius of the hollow cylinder is ‘R’ and the inner radius of the hollow cylinder be ‘r’

The Total surface area=