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 = 4/3πr³
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 = 1/3πr²h
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.
