Surface Area of Half Cylinder

The surface area of a half cylinder is the total area occupied by the boundary or surface of a half cylinder. It is measured in square units.

A half cylinder is a 3D shape made by slicing a cylinder along its length. It has a semicircular base, a flat rectangular surface, and a curved surface.

The surface area is the sum of these three parts:

the curved surface area, the rectangular area, and the semicircular base area.

Half cylinders are often used in architectural designs and engineering projects for their aesthetic appeal and structural properties.

A half cylinder has a curved surface and two flat surfaces. It has three components for its surface area: the curved surface area, the rectangular base area, and the semicircular base area.

Look at the diagram of a half cylinder below to see its surface area, height(h), and radius(r).

A half cylinder has three types of surface areas:

Curved Surface Area of a Half Cylinder

Rectangular Surface Area of a Half Cylinder

Semicircular Base Area of a Half Cylinder

The area of the curved part of the half cylinder is known as the curved surface area. The formula for the CSA (Curved Surface Area) of the half cylinder is given as:

Curved Surface Area = πrh square units

Here, r is the radius of the base of the half cylinder. h is the height of the half cylinder.

The total area occupied by the half cylinder, including the area of the curved surface, the rectangular surface, and the semicircular base, is known as the total surface area of the half cylinder.

The total surface area of a half cylinder is calculated by using the formula:

Total Surface Area = πrh + 2rh + ½πr² square units Where r is the radius of the base of the half cylinder. h is the height of the half cylinder.

Derivation of the Total Surface Area of a Half Cylinder

To find the total surface area of a half cylinder, imagine slicing it along its length and unfolding it. The curved surface forms a rectangle, the base is a semicircle, and there is a rectangular face.

Let us take a half cylinder with height(h) and radius of the base(r).

Total surface area of a half cylinder = curved surface area + rectangular base area + semicircular base area

Here, the curved surface area = πrh

Rectangular base area = 2rh

Semicircular base area = ½πr²

Adding these components gives: Total Surface Area = πrh + 2rh + ½πr²

The volume of a half cylinder shows how much space is inside it. It tells us how much space is inside the half cylinder or how much it can hold. The volume of a half cylinder can be found by using the formula: Volume = ½(πr²h) cubic units

Students often make mistakes while calculating the surface area of a half cylinder, leading to incorrect answers. Below are some common mistakes and the ways to avoid them.