Maths: Applications and Interpretation · Geometry and trigonometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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In three dimensions a point has three coordinates (x, y, z). The distance between two points is found with Pythagoras used on all three differences, and the midpoint is the average of each coordinate.
For solids you need the volume and surface area formulas for pyramids, cones, spheres and hemispheres. A combined solid is split into simple parts: add the volumes, but for surface area count only the faces that are on the outside.
To find an angle in a solid, draw a right-angled triangle inside it. The angle between a line and a plane is the angle between the line and its projection (its shadow) on that plane.
Students use the slant height in the volume formula of a cone or pyramid. Volume needs the vertical height h; the slant height l is only for the curved surface area.
Answer: 59.5° (to 3 significant figures)
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