Geometry and Measurement — Volume of pyramids and cones

About this lesson

This unit focuses on calculating the volumes of pyramids and cones. It begins by comparing the volume of a pyramid to a prism with the same base area and height, and a cone to a cylinder with the same base area and height, establishing that the volume of a pyramid or cone is one third of the corresponding prism or cylinder. The unit provides formulas, worked examples, and practice problems for finding volumes of regular pyramids (including quadrangular and pentagonal) and right cones, often requiring the use of the Pythagorean theorem to find heights from slant heights. It also includes problems involving converting solids (e.g., melting and recasting) and calculating capacities of containers in liters, with a note that 1 liter = 1000 cm³ = 1 dm³. By the end, students should be able to compute volumes of regular pyramids and right cones, solve real-life and mathematical problems involving these volumes, and handle conversions and capacity calculations.