Practice Flashcards
Flip to reveal answersA solid is given by coordinates. What's the first step?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Solids in 3D coordinates
Sign up free to track progress and get spaced-repetition review schedules.
Question
A solid is given by coordinates. What's the first step?
Answer
Turn the coordinates into lengths — use the 3D distance and midpoint formulas to find edges, radii and heights.
Question
How do you find the radius from a diameter [AB]?
Answer
Radius = ½ × the 3D distance AB; the centre is the midpoint of AB.
Question
How do you find a cone or pyramid's height from coordinates?
Answer
It's the distance from the apex to the centre of the base (a vertical drop), not a slant edge.
Question
Total surface area of a solid hemisphere, radius r?
Answer
3πr² — the curved dome 2πr² plus the flat base πr².
Question
Volume of a hemisphere, radius r?
Answer
⅔πr³ — half of a sphere's ⁴⁄₃πr³.
Question
Angle at a vertex between two edges, all three corners known?
Answer
Find the three side lengths with the distance formula, then use the cosine rule.
Question
Angle between a slant edge and the base?
Answer
tan θ = height ÷ (horizontal distance from the base centre to that corner).
Question
Exact or decimal?
Answer
Paper 1 usually wants exact (keep π and surds); Paper 2 round to 3 s.f.
Read the notes
Full study notes for Solids in 3D coordinates
Topic 3.1 hub
3D geometry
More from Topic 3.1
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free