Surface area of prisms and cylinders

key notes :

Surface Area Basics

• Surface area is the total area of all the faces of a 3D shape.
• It is measured in square units (e.g., cm², m²).

Surface Area of Prisms

A prism is a 3D shape with two identical parallel bases and rectangular or parallelogram lateral faces.

• Formula for Surface Area of a Prism:

Surface Area = 2 × Base Area + Lateral Area

• Lateral Area is the sum of the areas of all the side faces (excluding the bases).

Example:

For a rectangular prism (cuboid) with length (l), width (w), and height (h):

Surface Area = 2(lw + lh + wh)

Surface Area of Cylinders

A cylinder has two circular bases and a curved lateral surface.

Formula for Surface Area of a Cylinder:

Surface Area = 2πr² + 2πrh

Where:

• r = radius of the base
• h = height of the cylinder
• 2πr² = total area of the two circular bases
• 2πrh² = lateral (curved) surface area

Key Steps to Find Surface Area

• Identify the shape (prism or cylinder).
• Determine the dimensions (length, width, height, radius, etc.).
• Calculate the base area and lateral area separately.
• Add all the areas to get the total surface area.

Learn with an example

let’s practice!