Introduction to surface area and volume

key notes :

Understanding 3D Shapes

• Three-dimensional (3D) shapes have length, width, and height.
• Common 3D shapes include cubes, cuboids, cylinders, cones, spheres, and pyramids.

Surface Area

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

Types of Surface Area:

• Lateral Surface Area (LSA): The area of only the side faces (excluding top and bottom).
• Total Surface Area (TSA): The sum of all faces of the shape.

Volume

Volume is the space occupied by a 3D shape.

It is measured in cubic units (e.g., cm³, m³).

Formula for Volume:

• Cube: V = a³
• Cuboid: V = l × w × h
• Cylinder: V = πr² h
• Cone: V = 1/3 πr² h
• Sphere: V = 4/3 πr³

Relationship Between Surface Area and Volume

• Larger surface area allows for more exposure (e.g., heat transfer in objects).
• Volume determines the capacity of an object (e.g., how much liquid a container can hold).

Real-Life Applications

• Architecture and Construction (e.g., designing buildings and tanks).
• Packaging Industry (e.g., determining material for boxes and bottles).
• Medical Field (e.g., calculating drug dosage in medicine bottles)

Learn with an example

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