How to Calculate the Volume of Pyramids and Cones

Miacademy & MiaPrep Learning Channel

This educational video guides students through the derivation and application of volume formulas for pyramids and cones by comparing them to prisms and cylinders. The narrator, Justin, uses visual animations to demonstrate that a pyramid or cone holds exactly one-third the volume of a prism or cylinder with the same base area and height. This visual proof helps students move beyond simple memorization to a conceptual understanding of why the "one-third" fraction appears in these geometric formulas. The content covers key geometric concepts including base area (represented as 'Big B'), height versus slant height, and volume calculation. A significant portion of the video is dedicated to distinguishing between the perpendicular height needed for calculations and the slant height, a common source of student errors. The lesson progresses from conceptual theory to a practical application problem where students must select the correct dimensions to calculate the volume of a specific cone. For educators, this video serves as an excellent bridge between 2D area concepts and 3D volume applications. It is particularly useful for introducing the volume formulas for pyramids and cones, as the water-filling animation provides a memorable visual anchor for the 1:3 ratio. The step-by-step walkthrough of an example problem also provides a model for student work, emphasizing the importance of identifying the correct variables and avoiding distractors like slant height.