This page covers more complex geometric shapes, including pyramids, spheres, and cones, providing formulas and examples for calculating their volumes.

Pyramid Volume

The volume of a pyramid is calculated using the formula:

Volume = 1/3 × Base Area × Height

Example: For a square-based pyramid with base side 8cm and height 12cm: Volume = 1/3 × 8 × 8 × 12 = 256 cm³

Sphere Volume

The formula for volume of a sphere with radius r is:

Volume = 4/3 × π × r³

Example: For a sphere with radius 5cm: Volume = 4/3 × π × 5³ ≈ 523.6 cm³ (rounded to one decimal place)

Cone Volume

The volume of a cone is calculated using the formula:

Volume = 1/3 × π × r² × h

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

Example: For a cone with radius 3cm and height 8cm: Volume = 1/3 × π × 3² × 8 ≈ 75.4 cm³ (rounded to one decimal place)

Highlight: These formulas are essential for solving complex geometry problems and understanding three-dimensional shapes in mathematics and science.

This page introduces the concept of volume and provides formulas and examples for calculating the volume of various geometric shapes. The focus is on cubes, cuboids, and triangular prisms.

Definition: Volume is the amount of three-dimensional space occupied by an object, typically measured in cubic units such as cm³ or m³.

Cube Volume

The formula for the volume of a cube is:

Volume = Length × Width × Height

Example: For a cube with sides of 6cm, the volume calculation is: Volume = 6 × 6 × 6 = 216 cm³

Cuboid Volume

The volume of a cuboid (rectangular prism) is calculated using the same formula as a cube:

Volume = Length × Width × Height

Example: For a cuboid with dimensions 8cm × 4cm × 5cm, the volume is: Volume = 8 × 4 × 5 = 160 cm³

Triangular Prism Volume

The volume of a triangular prism is calculated by multiplying the area of the triangular face by the length of the prism:

Volume = (Base × Height ÷ 2) × Length

Example: For a triangular prism with a base of 6cm, height of 5cm, and length of 15cm: Volume = (6 × 5 ÷ 2) × 15 = 225 cm³

Cylinder Volume

The formula for the volume of a cylinder with radius r and height h is:

Volume = π × r² × h

Highlight: When using a calculator, π is often represented by the 'shift' function followed by X10.

Example: For a cylinder with radius 4.8cm and height 14cm: Volume = π × 4.8² × 14 ≈ 1013.35 cm³ (rounded to two decimal places)