Prisms, Cones, Spheres, and Pyramids: Volume Formulas

This page introduces the volume formulas for all shapes commonly encountered in geometry, focusing on prisms, cones, spheres, and pyramids. These formulas are crucial for solving GCSE volume questions and answers.

Prisms are defined as three-dimensional shapes with a constant cross-section throughout their length. Examples include cylinders, cuboids, and hexagonal prisms. The volume formula for prisms is:

Definition: Volume of a prism = cross-section area × perpendicular length

For cylinders, a specific type of prism, the formula is:

Formula: Volume of a cylinder = πr²h

Where r is the radius of the base and h is the height of the cylinder.

An example calculation for a cylinder with radius 8 cm and height 10 cm is provided:

Example: V = π × 8² × 10 = 2010.6 cm³

The page also covers the volume formula for spheres:

Formula: Volume of a sphere = (4/3)πr³

An example calculation for a sphere with radius 5 cm is shown:

Example: V = (4/3) × π × 5³ = 523.6 cm³

For cones, the volume formula is:

Formula: Volume of a cone = (1/3)πr²h

An example calculation for a cone with radius 8 cm and height 13.2 cm is provided:

Example: V = (1/3) × π × 8² × 13.2 = 884.7 cm³

Highlight: These formulas are typically provided on GCSE exam papers, but understanding their application is crucial for solving problems effectively.