Learn 3D Geometry: 77 Flashcards for Volume, Surface Area and the Platonic Solids
Master 3D geometry with 77 Flip It flashcards: volume and surface area formulas for cubes, cylinders, cones, spheres, frustums and the five Platonic solids.
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Volume and surface area are where geometry stops being about drawing and becomes substitution discipline. Students rarely lose points because they forgot that a sphere is (4/3)πr³ — they lose them by grabbing the diameter instead of the radius, or the cone's height where the slant height belonged. The 3D Geometry: Volume & Surface Area deck (code XQ5303, 77 cards) on Flip It drills both halves: the vocabulary of solids, and the formulas with worked numbers attached.
Study this deck: 3D Geometry: Volume & Surface Area
1 / 10Solid geometry
Tap the card for the answer · swipe right if you knew it, left if not
What the deck actually covers
It moves from naming solids to computing them. You'll drill: solid geometry (stereometry), polyhedra, prisms, pyramids, cubes, cuboids, parallelepipeds, tetrahedra, octahedra, dodecahedra, icosahedra, the five Platonic solids, cylinders, cones, spheres and balls, frustums, ellipsoids, spheroids, solids of revolution, paraboloids, hyperboloids, tori, dihedral and solid angles, steradians, Euler's formula, Cavalieri's principle, convexity, and descriptive versus projective geometry.
Sample cards
| Front | Back |
|---|---|
| Volume formula for a sphere | V = (4/3)πr³ |
| Surface area formula for a cone | SA = πr² + πrl, where r is radius and l is slant height |
| Slant height of a cone | The distance from the apex to a point on the edge of the base (l = √(r² + h²)) |
| If a cylinder has radius 3 and height 5, what is its volume? | 45π ≈ 141.37 (V = π × 3² × 5) |
| How does a pyramid's volume compare to a prism with the same base and height? | A pyramid has 1/3 the volume of a prism with the same base and height |
| Euler's formula for polyhedra | V − E + F = 2, where V = vertices, E = edges, F = faces (for convex polyhedra) |
| Cavalieri's principle | If two solids have equal cross-sectional areas at every height, they have equal volumes |
| Diagonal of a cube with side s | s√3 (space diagonal through the interior) |
| Volume of a torus | V = 2π²Rr², where R is the major radius and r is the minor radius |
| Frustum | A cone or pyramid with the top cut off by a plane parallel to the base |
Two tips that fit this deck specifically
Group the formulas by their 1/3. The deck gives prism V = B×h and pyramid V = (1/3)B×h; cylinder V = πr²h and cone V = (1/3)πr²h. One family: the pointed solid is a third of the straight solid on the same base. Four base cases plus the 1/3 rule covers a dozen cards. Only the sphere pair — V = (4/3)πr³, SA = 4πr² — the torus and the cone frustum need memorising cold.
Answer the numeric cards in exact form first. "If a sphere has radius 3, what is its volume?" → 36π ≈ 113.10. Say "36 pi" before "113": exams usually want the π form, and it's the last step where a substitution error is still visible — once you've written 113.10 the mistake is buried.
One deck quirk: the numeric answers are bare numbers (64, 54, 24), no units. Add "cubic units" for volumes and "square units" for areas in your head every time — dimensional mismatch is the cheapest point to lose. A few cards also repeat by design: cuboid and rectangular prism carry the same V = l × w × h and SA = 2(lw + lh + wh) under two names. Free reinforcement of the naming, not a new formula.
Run the core volume and surface-area block first — that's the exam-bearing part. Save the Platonic solids, tori and hyperboloids for a second pass.
Study this deck on Flip It — search the library for 3D Geometry: Volume & Surface Area (XQ5303) once you're logged in.
Related: Master Triangles & Polygons: 136 Geometry Flashcards from Centroids to Pick's Theorem
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