Volume of prisms and cylinders

key notes :

Definition of 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 solid with two identical bases and rectangular lateral faces.
• Formula:

V = B × h

where:

B = Area of the base

h = Height of the prism

Types of Prisms:

Rectangular Prism: V = l × w × h

Triangular Prism: V = 12 × b × h_base × h_prism

Volume of a Cylinder

A cylinder is a 3D shape with two circular bases and a curved surface.

Formula:

V = πr²h

where:

r = Radius of the circular base

h = Height of the cylinder

π ≈ 3.1416

Comparing Prisms and Cylinders

• Both follow the general volume formula: Base Area × Height
• A prism has polygonal bases, while a cylinder has circular bases.

Key Problem-Solving Steps

• Identify the shape (prism or cylinder).
• Find the base area (BBB) using appropriate formulas.
• Multiply the base area by the height (hhh).
• Use proper units and round off answers if necessary.

Example Problems

Find the volume of a rectangular prism with dimensions 5 cm × 4 cm × 10 cm.

V = 5 × 4 × 10 = 200 cm3

Calculate the volume of a cylinder with radius 7 cm and height 12 cm.

V = π (7²)(12) = π(49)(12) = 588π ≈ 1847.52 cm³

Learn with an example

let’s practice!