WEBVTT 00:00:00.500 --> 00:00:03.868 Welcome to GCSE Edexcel Maths revision. 00:00:04.018 --> 00:00:07.712 Topic M 31: Solids, surface area and volume. 00:00:07.862 --> 00:00:10.657 This video covers Foundation and Higher tiers. 00:00:13.333 --> 00:00:18.113 A face is a surface, an edge is where faces meet, and a vertex is a corner. 00:00:18.263 --> 00:00:22.243 A cuboid has 6 faces, 12 edges and 8 vertices. 00:00:22.393 --> 00:00:26.113 A sphere has one curved surface and no edges or vertices. 00:00:28.767 --> 00:00:31.965 A prism has a constant cross-section along its length. 00:00:32.115 --> 00:00:36.166 A pyramid has a base and triangular faces meeting at an apex. 00:00:36.316 --> 00:00:40.701 Cylinders and cones have curved surfaces, so not every face is flat. 00:00:43.367 --> 00:00:48.338 A plan is the view from above; an elevation is a specified side or front view. 00:00:48.488 --> 00:00:53.159 Draw the visible outline using the given dimensions, not a perspective sketch. 00:00:53.309 --> 00:00:55.699 Cuboid plan and front elevation 00:01:00.367 --> 00:01:07.907 Volume measures space occupied and uses cubic units; surface area totals the external surfaces and uses square units. 00:01:08.057 --> 00:01:13.197 Capacity may use litres, with 1 litre equals 1000 cubic centimetres . 00:01:15.867 --> 00:01:18.767 Volume of a cuboid equals l w h. 00:01:18.917 --> 00:01:24.302 Volume of a prism equals cross-sectional area multiplied by perpendicular length. 00:01:24.452 --> 00:01:27.351 A cylinder has V equals pi r squared h. 00:01:30.033 --> 00:01:34.597 Worked example: A triangular prism with triangle base 4 centimetres, 00:01:34.747 --> 00:01:48.367 perpendicular height 3 centimetres and prism length 8 centimetres has volume open bracket 1 over 2 multiplied by 4 multiplied by 3 close bracket multiplied by 8 equals 48 cubic centimetres . 00:01:51.033 --> 00:01:57.625 A pyramid has V equals 1 over 3 multiplied by base area multiplied by perpendicular height. 00:01:57.775 --> 00:02:01.386 A cone has V equals 1 over 3 pi r squared h. 00:02:01.536 --> 00:02:04.618 Slant height is not the height in these volume formulae. 00:02:07.300 --> 00:02:16.440 In a right circular cone, perpendicular height h, radius r and slant height l form a right triangle: l squared equals h squared plus r squared . 00:02:16.590 --> 00:02:19.747 Use h for volume and l for curved surface area. 00:02:19.897 --> 00:02:22.649 Perpendicular height and slant height in a cone 00:02:27.300 --> 00:02:30.692 A sphere has V equals 4 over 3 pi r cubed . 00:02:30.842 --> 00:02:35.027 A hemisphere has half this volume: 2 over 3 pi r cubed . 00:02:37.700 --> 00:02:51.565 Worked example: A cone with radius 3 centimetres and perpendicular height 8 centimetres has volume 1 over 3 multiplied by pi multiplied by 9 multiplied by 8 equals 24 pi cubic centimetres . 00:02:54.233 --> 00:02:59.619 Surface area of a cuboid is 2 l w plus 2 l h plus 2 w h. 00:02:59.769 --> 00:03:04.749 A net helps identify every face and avoid counting a hidden internal join. 00:03:04.899 --> 00:03:07.352 A net with all six cuboid faces 00:03:12.033 --> 00:03:21.185 For a closed cylinder, total surface area is 2 pi r squared plus 2 pi rh: two circular ends and one curved rectangular surface. 00:03:21.335 --> 00:03:24.667 An open-top cylinder has only one circular end. 00:03:27.333 --> 00:03:31.749 A cone's curved surface area is pi rl, where l is slant height. 00:03:31.899 --> 00:03:36.551 Add pi r squared for its circular base when finding total surface area. 00:03:39.233 --> 00:03:42.263 A sphere's surface area is 4 pi r squared . 00:03:42.413 --> 00:03:49.857 A hemisphere has curved area 2 pi r squared , or total area 3 pi r squared if its circular base is included. 00:03:52.533 --> 00:04:06.964 Worked example: A closed cylinder of radius 2 centimetres and height 5 centimetres has volume 20 pi cubic centimetres and total surface area 8 pi plus 20 pi equals 28 pi square centimetres . 00:04:09.633 --> 00:04:14.443 For composite volumes, add non-overlapping parts or subtract a removed region. 00:04:14.593 --> 00:04:18.775 For composite surface areas, omit faces hidden where parts join. 00:04:18.925 --> 00:04:21.654 State which surfaces the question requires. 00:04:24.333 --> 00:04:27.201 That completes Solids, surface area and volume. 00:04:27.351 --> 00:04:30.696 Revisit the notes and test yourself on the revision website.