https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/a/cavalieri-s-principle-in-2d 2022-10-27T00:15:07.305964705Z Cavalieri's principle in 2D If two figures have the same height and the same width at every point along that height, they have the same area. article https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/a/cavalieri-s-principle-in-3d 2023-07-25T19:17:13.180252954Z Cavalieri's principle in 3D If two 3D figures have the same height and the same cross-sectional area at every point along that height, they have the same volume. article https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/v/cavalieris-principle-in-3d 2022-09-10T02:03:40.164764806Z Cavalieri's principle in 3D Cavalieri's principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/e27e124a-9e63-404c-9be0-9b6296d1bbbe_1280_720_base.png Cavalieri's principle in 3D Cavalieri's principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume. https://cdn.kastatic.org/ka-youtube-converted/2TDFtCKMoKk.mp4/2TDFtCKMoKk.mp4 296 Cavalieri's principle and dissection methods https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/e/explain-related-volumes 2022-09-10T02:03:40.164764806Z Apply Cavalieri's principle Determine when it is appropriate to apply Cavalieri's principle and use it to justify why certain figures have equal volumes. exercise https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/v/volume-of-pyramids-intuition 2022-09-10T02:03:40.164764806Z Volume of pyramids intuition The volume of a pyramid is a fraction of the volume of the rectangular prism that encloses it. We can find out what that fraction is by cutting a prism into several pyramids. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/54086373-166b-4254-af88-47d3cb8c8dd9_1280_720_base.png Volume of pyramids intuition The volume of a pyramid is a fraction of the volume of the rectangular prism that encloses it. We can find out what that fraction is by cutting a prism into several pyramids. https://cdn.kastatic.org/ka-youtube-converted/fD52yzLF8DA.mp4/fD52yzLF8DA.mp4 509 Cavalieri's principle and dissection methods https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/a/volume-of-a-pyramid-or-cone 2022-10-27T00:15:07.305964705Z Volume of a pyramid or cone Where does the 1/3 come from in the formula for the volume of a pyramid? How does the volume of a cone relate? What about oblique pyramids (pyramids that lean to the side)? article https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/v/volumes-of-cones-intuition 2022-09-10T02:03:40.164764806Z Volumes of cones intuition Use Cavalieri's Principle to establish that the formula for the volume of a cone is the same as the formula for the volume of a pyramid (1/3 * base area * height). Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/d4449373-474c-49d7-9c95-f6f5c9ea9b96_1280_720_base.png Volumes of cones intuition Use Cavalieri's Principle to establish that the formula for the volume of a cone is the same as the formula for the volume of a pyramid (1/3 * base area * height). https://cdn.kastatic.org/ka-youtube-converted/LmBViMOeYXg.mp4/LmBViMOeYXg.mp4 342 Cavalieri's principle and dissection methods https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/v/using-related-volumes 2022-09-10T02:03:40.164764806Z Using related volumes Use related volumes (using the volume of one figure to determine the volume of another). Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/94b2748f-1ad4-43f7-ac91-e7f262fd8cf2_1280_720_base.png Using related volumes Use related volumes (using the volume of one figure to determine the volume of another). https://cdn.kastatic.org/ka-youtube-converted/knNLHsjIcl8.mp4/knNLHsjIcl8.mp4 376 Cavalieri's principle and dissection methods https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/e/use-related-volumes 2024-05-31T20:12:33.437983911Z Use related volumes Scale, dissect, and rearrange simpler figures to help find the volume of more complicated figures, including pyramids, oblique figures, and figures with different base shapes. exercise https://www.khanacademy.org/math/geometry/hs-geo-solids/xff63fac4:hs-geo-cavalieri-s-principle/e/volume-of-prisms-and-pyramids 2026-04-01T19:51:47.642074865Z Volume of prisms and pyramids No matter what shape the base is, if we know the height and the area of the base of prism-like or pyramid-like solids, we can find their volume. exercise