3D Geometry Fundamentals and Formulas

Think of surface area as the amount of wrapping paper you'd need to cover a gift box completely - it's the total area of all the outside surfaces combined. Volume, on the other hand, tells you how much stuff can actually fit inside that box.

When working with 3D shapes, the base isn't always the bottom - it's whatever flat surface we use as our reference point. The height is always measured straight up from the base at a 90-degree angle, never slanted.

Cubes and rectangular prisms are your starting point for understanding 3D geometry. A cube uses the formula SA = 6s² for surface area (since all six faces are identical squares) and V = s³ for volume. Rectangular prisms get more complex with SA = 2lw + 2lh + 2wh and V = lwh.

Quick Tip: For any right prism, you can find volume by multiplying the base area by the height $V = Bh$. This works whether your base is a triangle, rectangle, or any other shape!

Cylinders follow similar patterns to prisms but use π in their formulas. Surface area becomes SA = 2πr² + 2πrh, while volume stays relatively simple at V = πr²h. The key is remembering that cylinders have two circular ends plus the curved side surface.