Solid geometry
10 videos
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17
Geometry - Welcome to Solid Geometry
Learn to measure 3D shapes through cross-sections, volume formulas, and density. Discover how to slice shapes, calculate space, and connect mass to volume.
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6
Geometry - Cross-Sections of 3D Shapes
Learn how cross-sections work by slicing 3D objects at different angles to create various 2D shapes like squares, rectangles, triangles, and hexagons.
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8
Geometry - Rotating 2D Shapes into 3D Solids
Learn how spinning 2D shapes around an axis creates 3D solids of revolution, like cylinders from rectangles and cones from triangles.
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3
Geometry - Cavalieri's Principle Explained
Explains Cavalieri's Principle: if two 3D shapes have equal height and identical cross-sectional areas at every level, they have the same volume, regardless of appearance.
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7
Geometry - Volume of Prisms and Cylinders
Learn the universal volume formula V = B × h for prisms and cylinders, with examples using rectangular prisms and cylinders to calculate volume step by step.
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6
Geometry - Calculating Cylinder Volume and Surface Area
Learn to calculate volume and surface area of cylinders using a water bottle example. Covers formulas, step-by-step calculations, and the difference between cubic and square units.
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9
Geometry - Volume of Pyramids and Cones — The 1/3 Rule
Learn why pyramids and cones have volume equal to one-third base times height, with visual proof and a worked example calculating cone volume.
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13
Geometry - Volume of a Sphere
Learn how to calculate the volume of a sphere using the formula V = 4/3πr³, including how to convert diameter to radius and solve example problems.
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14
Geometry - Solving a Real-World Volume Problem
Learn to calculate fill time for a composite solid (cylinder + cone) using volume formulas and rate conversions. Practical application of geometry to real-world problems.
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9
Geometry - Density: Connecting Mass, Volume, and Area
Learn what density means in math: quantity per space. Covers area and volume density formulas, with real-world examples like concerts, trees, and steel vs foam balls.