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Spatial Geometry

Pyramids, cones, cylinders, planes, distances and 3D angles.

25 lessons

1Pyramid volume: identify the base and perpendicular heightSpatial Geometry · Ms Tam · V = (1/3) × base area × perpendicular height2Distance from a point to a plane using volumeSpatial Geometry · Ms Tam · V = (1/3) × base area × height3Finding the angle between a line and a planeSpatial Geometry · Ms Tam · θ = angle between the line and its projection4Writing the equation of a plane in 3DSpatial Geometry · Mr Wong · Ax + By + Cz + D = 05Cylinder volume and curved surface areaSpatial Geometry · Ms Tam · V = πr²h6Cone volume when slant height is givenSpatial Geometry · Ms Tam · l² = r² + h²7Prism volume from a cross-sectionSpatial Geometry · Ms Tam · V = cross-sectional area × length8Sphere volume without the fear of πSpatial Geometry · Ms Tam · V = (4/3)πr³9Space diagonal of a cubeSpatial Geometry · Mr Wong · face diagonal = a√210Volume of a triangular pyramidSpatial Geometry · Ms Tam · V = (1/3) × triangle area × height11Frustum of a pyramid: the cut-off topSpatial Geometry · Ms Tam · V = (1/3)h(A₁ + A₂ + √(A₁A₂))12Angle between two planesSpatial Geometry · Ms Ho · cos φ = |n₁ · n₂| / (|n₁||n₂|)13Shortest distance between skew linesSpatial Geometry · Mr Wong · d = |(P₂−P₁) · n| / |n|14Largest cylinder inside a sphereSpatial Geometry · Ms Tam · r² + (h/2)² = R²15Cube nets and surface areaSpatial Geometry · Ms Ho · surface area = 6a²16Finding height from a lateral edgeSpatial Geometry · Ms Tam · h = √(ℓ² − d²)17Plane determined by three pointsSpatial Geometry · Mr Wong · n = AB × AC18Hemisphere volume and curved surfaceSpatial Geometry · Ms Tam · V = (2/3)πr³19Space diagonal of a rectangular boxSpatial Geometry · Mr Wong · d = √(a² + b² + c²)20Volume of a hollow pipeSpatial Geometry · Ms Tam · V = π(R² − r²)h21True height from an oblique sketchSpatial Geometry · Ms Ho · mark ⊥ before measuring height22Cone: from slant height to perpendicular heightSpatial Geometry · Ms Tam · ℓ² = r² + h²23Composite solids: add or subtract volumesSpatial Geometry · Ms Tam · V_total = V₁ ± V₂ ± …24Circular cross-section of a sphereSpatial Geometry · Mr Wong · ρ = √(R² − d²)25Surface area of a square-based pyramidSpatial Geometry · Ms Ho · total SA = a² + 2aℓ