Surface Area of Elliptical Cylinder

The surface area of an elliptical cylinder is the total area occupied by the boundary or surface of an elliptical cylinder.

It is measured in square units.

An elliptical cylinder is a 3D shape with an elliptical base and a specific height.

Unlike a circular cylinder, where the base is a circle, an elliptical cylinder has an oval base.

The surface area includes the curved surface and the base areas.

An elliptical cylinder does not have variations like a cone but can have different base dimensions (major and minor axes).

An elliptical cylinder has a curved surface, and it has two types of surface areas: the curved surface area and the total surface area.

Look at the elliptical cylinder below to see its surface area, height (h), major axis (a), and minor axis (b).

An elliptical cylinder has two types of surface areas:

Curved Surface Area of an Elliptical Cylinder

Total Surface Area of an Elliptical Cylinder

The area of the curved part of the elliptical cylinder, excluding its bases, is known as the curved surface area of an elliptical cylinder.

The formula for the CSA (Curved Surface Area) of the elliptical cylinder is given as:

Curved Surface Area = 2πah square units

Here, a is the semi-major axis of the base ellipse, and h is the height of the cylinder.

The total area occupied by the elliptical cylinder, including the area of the curved surface and the area of the elliptical bases, is known as the total surface area.

The total surface area of an elliptical cylinder is calculated by using the formula:

Total surface area = 2πa(h + b) square units Where a is the semi-major axis of the base, b is the semi-minor axis of the base, and h is the height of the cylinder.

Derivation of the Total Surface Area of an Elliptical Cylinder: To find the total surface area of an elliptical cylinder, imagine cutting it along its height and unfolding it.

The curved surface area is a rectangle, and the total surface area includes the areas of the two elliptical bases.

Total surface area of an elliptical cylinder = base areas + curved surface area

Here, the base area of an ellipse = πab

Curved surface area = 2πah

Substituting the formulas into the total surface area,

Total surface area = 2πab + 2πah

Take the common terms out: T = 2πa(b + h)

Therefore, the total surface area of the elliptical cylinder T = 2πa(b + h)

The volume of an elliptical cylinder shows how much space is inside it. It tells us how much space is inside or how much it can hold.

The volume of an elliptical cylinder can be found by using the formula: Volume = πabh cubic units

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