Volume measures the space occupied by a solid; surface area is the total area of its faces.
1Cuboid and cube
Cuboid: V = lbh, TSA = 2(lb + bh + hl), diagonal = √(l² + b² + h²)
Cube: V = a³, TSA = 6a², diagonal = a√3
2Cylinder, cone, sphere
Cylinder: V = πr²h, CSA = 2πrh, TSA = 2πr(h + r)
Cone: V = (1/3)πr²h, slant height l = √(r² + h²), CSA = πrl
Sphere: V = (4/3)πr³, SA = 4πr²; hemisphere: V = (2/3)πr³, TSA = 3πr²
3Melting and recasting
The volume stays the same: number of small solids = big volume ÷ small volume