3D Solid Figures
Volume and surface area of prisms, cylinders, cones, pyramids, and spheres.
This page is a free outline of what the 3D Solid Figures lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Scale Factor – Volume and Surface Area
- Composite Shapes (3D) A composite solid is built from simpler solids; find its volume by splitting it into familiar pieces (a cylinder plus a cone, say) and adding their volumes.
- Cone – Surface Area The surface area of a cone is πr² + πrℓ — the circular base plus the slanted side, where ℓ is the slant height.
- Cone – Volume The volume of a cone is ⅓πr²h — exactly one-third of a cylinder with the same base and height.
- Cylinder – Surface Area The surface area of a cylinder is 2πr² + 2πrh — the two circular ends plus the rolled-up side wall around them.
- Cylinder – Volume
- Properties of 3-D Solids Solids are told apart by their faces, edges, and vertices — a cube has 6 flat faces, a cylinder has two circular ends and a curved side, a sphere is one smooth surface.
- Pyramid – Surface Area The surface area of a pyramid is its base area plus the areas of the triangular faces that rise to the apex.
- Pyramid – Volume The volume of a pyramid is ⅓ × base area × height — one-third of a prism with the same base and height.
- Rectangular Prism – Surface Area The surface area of a rectangular prism (box) is the total area of its six faces: 2(lw + lh + wh) — how much material covers the outside.
- Rectangular Prism – Volume
- Sphere – Surface Area The surface area of a sphere is 4πr² — the area of its curved outer skin.
- Sphere – Volume The volume of a sphere is (4/3)πr³ — the space inside a ball, set entirely by its radius.
Linked concepts (purple →) have a full explanation. Hover or tap a dotted ⓘ concept for a quick definition.
Inside the app, 3D Solid Figures comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
Practice 3D Solid Figures with your AI Tutor
Interactive lessons, quizzes, and a 24/7 AI Tutor — every answer verified by three independent AI systems. Currently free for individual users.
Create your free account →