Volume of prisms and cylinders

key notes :

Understanding Volume

• Volume is the amount of space occupied by a 3D object.
• It is measured in cubic units (e.g., cm³, m³).

Volume of a Prism

A prism is a 3D shape with two identical, parallel bases and rectangular sides.

Formula:

Volume = Base Area × Height

Types of prisms:

• Rectangular prism:

V = l × w × h

• Triangular prism:

V = 1/2 × Base × Height × Prism Height

Volume of a Cylinder

A cylinder has circular bases and a curved surface.

Formula: V=πr2hV = \pi r^2 hV=πr2h where:

• r = radius of the base
• h = height of the cylinder
• π≈3.14 or 22/7

Key Concepts

• Base area: The area of the shape forming the base of the prism or cylinder.
• Height: The perpendicular distance between the bases.
• Units: Always use cubic units for volume (e.g., cm³, m³).

Real-Life Applications

• Measuring the capacity of tanks, pipes, and boxes.
• Calculating the amount of material needed for construction.
• Understanding storage space in packaging.

Learn with an example

let’s practice!