3D Shapes- Volume

3D Shapes- Volume

Basic Principles for Calculating Volume

• Volume is the amount of space a 3D shape occupies, often measured in cubic units (cm³, m³ etc.).
• Calculating volume involves understanding the structure of the 3D shape, and multiplying its dimensions.
• Different 3D shapes require different formulas for their volume calculation.

Formulas for Volume Calculation

Cubes and Cuboids

• The volume, V, of a cube or cuboid is obtained by multiplying the length (l), the width (w), and the height (h): V = lwh.
• A cube is a special type of cuboid where all sides are equal. Thus, the volume, V, of a cube can be calculated as the cube of one of its side lengths (s): V = s³.

Cylinders

• The volume, V, of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height.
• Remember to use the correct value for π; use 3.14 or the “π” button on your calculator.

Cones

• The volume, V, of a cone is calculated as V = 1/3πr²h, where r is the radius of the base and h is the height.

Spheres

• The volume, V, of a sphere is given by V = 4/3πr³, where r is the radius.

Volume Conversion

• Be aware of units used and be able to convert between them.
• For example, to convert cm³ to m³, divide by 1,000,000 (not by 100).

Key Principles to Remember

• Always pay close attention to the units used in the problem and perform any necessary unit conversions before calculating the volume.
• Remember to keep your workings accurate and clear.
• Using a calculator, always check that you’ve entered the formula correctly.
• Practice various problems to understand volume calculations of complex shapes which require breaking down into simpler shapes.