What is the formula to find the total surface area?

The formula depends on the 3D shape. Here are the total surface area (TSA) formulas for common solids:

  • Cube: TSA = $6a^2$ (where $a$ is the edge length)
  • Rectangular prism (box): TSA = $2(ab + bc + ac)$ (edges $a,b,c$)
  • Sphere: TSA = $4\pi r^2$ (radius $r$)
  • Right circular cylinder: TSA = $2\pi r^2 + 2\pi r h$ (two circular bases plus curved surface; radius $r$, height $h$)
  • Right circular cone: TSA = $\pi r^2 + \pi r l$ (base area $+\,$lateral area; $r$ = base radius, $l$ = slant height)
  • Right prism (general): TSA = $2B + Ph$ (where $B$ = area of one base, $P$ = perimeter of the base, $h$ = prism height)
  • Pyramid (regular or not): TSA = $B + \tfrac{1}{2}Pl$ (base area $B$, perimeter of base $P$, slant height $l$)
  • Hemisphere: curved surface = $2\pi r^2$; including base (flat face) TSA = $3\pi r^2$.

If you meant a specific solid, tell me which one and I’ll show a worked example.

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