Volume

• Volume refers to the amount of space that a 3-dimensional object or shape occupies.
• The basic unit of volume in the metric system is the cubic meter (m³) but litres (l) and millilitres (ml) are commonly used for liquid measures.
• Volume can be found by multiplying the length, width, and height of a cube or cuboid. This is often given by the formula: V = lwh, where l is length, w is width and h is height.
• The volume of a cylinder is found by multiplying the area of its circular base by its height. The formula is often given as V = πr²h, where r is the radius of the base, and h is the height.
• The volume of a pyramid is 1/3 times the area of the base times the height. The formula is V = 1/3b×h, where b is the area of the base, and h is the height.
• The volume of a cone is similar to that of a pyramid, and it equals 1/3 times the area of the base times the height. This can be represented as V = 1/3πr²h, where r is the radius of the base and h is the height.
• The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere.
• The concepts of volume often include real-world applications such as solving problems regarding the capacity of liquids in containers, space usage, and material usage in manufacturing.
• Deep understanding of volume is strengthened by relating with area and surface area, practicing calculations, problem-solving tasks and real-world examples.
• Many real-world volume problems involve conversions between different units of measurement. Note that there are 1,000 cubic centimeters in a liter, and 1,000 liters in a cubic meter.

Always ensure to practice with a variety of questions, ranging from simple calculations to more complex problem-solving tasks.