Geometry: Surface Area and Volume of 3D Shapes

Vocabulary flashcards covering the shapes and formulas for surface areas and volumes mentioned in the notes, including LSA, CSA, TSA, and slant height.

Cube

A six-faced solid with all faces as equal squares. LSA = 4a^2; TSA = 6a^2; Volume = a^3.

Cuboid

A box with rectangular faces. LSA = 2h(l + b); TSA = 2(lb + bh + hl); Volume = l × b × h.

Sphere

A perfectly round solid. Surface Area = 4πr^2; Volume = (4/3)πr^3; its volume is about 2/3 that of a cylinder with the same radius and height (2r).

Hemisphere

Half of a sphere. CSA = 2πr^2; TSA = 3πr^2; Volume = (2/3)πr^3.

Right Circular Cylinder

Cylinder. CSA = 2πrh; TSA = 2πr(h + r); Volume = πr^2h.

Right Circular Cone

Cone. CSA = πrl; TSA = πr(l + r); Volume = (1/3)πr^2h. Slant height l comes from Pythagoras: l^2 = r^2 + h^2.

Slant height

The slanted side length of a cone, l, with l^2 = r^2 + h^2 (Pythagoras).

Lateral Surface Area (LSA)

Surface area excluding the top and bottom bases. Examples: cube LSA = 4a^2; cuboid LSA = 2h(l + b).

Curved Surface Area (CSA)

Area of the curved portion of a solid (no bases). Examples: hemisphere CSA = 2πr^2; cone CSA = πrl.

Total Surface Area (TSA)

Sum of areas of all faces of a solid. Examples: cube TSA = 6a^2; cylinder TSA = 2πr(h + r); sphere TSA = 4πr^2.

Volume

The amount of space contained inside a 3D shape. Units are cubic (e.g., cm^3, m^3).