Surface area of prisms and cylinders

key notes :

Definition of Surface Area

• The surface area of a 3D shape is the total area of all its faces.
• Measured in square units (e.g., cm², m²).

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Surface Area of a Prism

A prism is a 3D shape with two parallel and congruent bases.

Surface area (SA) of a prism = Lateral Surface Area (LSA) + Area of Two Bases.

Formula:

SA = Perimeter of Base × Height + 2 × Area of Base

Types of Prisms:

• Rectangular Prism:

SA = 2(lw + lh + wh)

• Triangular Prism:

SA = (Perimeter × Height) + 2 × 1/2 × Base × Height of Triangle

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Surface Area of a Cylinder

A cylinder has two circular bases and a curved surface.

Formula: SA = 2πrh + 2πr²

where:

• r = radius of the base
• h = height of the cylinder

The first term (2πrh) represents the lateral surface area.

The second term (2πr²) accounts for the areas of the two circular bases.

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Steps to Calculate Surface Area

• Identify the shape (prism or cylinder).
• Find the required dimensions (length, width, height, radius, etc.).
• Use the appropriate formula.
• Solve step by step, ensuring correct units.

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Real-Life Applications

• Prisms: Packaging boxes, aquariums, storage containers.
• Cylinders: Cans, pipes, water tanks.

Learn with an example

let’s practice!