Essential 3D Geometry Formulas

When working with 3D shapes, you need to know how to find both their volume (the space inside) and surface area (the total area covering the outside). These formulas are your toolkit for solving geometry problems!

For a sphere, which is perfectly round like a ball, the volume formula is V = 4/3πr³, where r is the radius. The surface area of a sphere is 4πr². These formulas apply to objects like basketballs, planets, and marbles.

A prism has identical shapes at both ends connected by flat faces. Its volume is simply V = Bh, where B is the area of the base and h is the height. For surface area, you add up all the faces. Prisms include boxes, triangular prisms, and many buildings.

Pro Tip: When calculating volume, think of it as "area of the base × height" for most shapes except spheres. This pattern makes formulas easier to remember!

Cones and cylinders both have circular bases. A cylinder's volume is V = Bh or πr²h, while a cone's volume is V = 1/3Bh or 1/3πr²h. Notice that a cone's volume is exactly one-third of a cylinder with the same base and height! For surface area, a cylinder includes its two circular bases plus the curved surface, while a cone has one circular base plus its curved surface $πr² + πrl, where l is the slant height$.