Gaynell Moss
Learning 3D shapes is fun
this is i poster i found very useful in teaching my son the differences between 3D shapes cubes, cones, sphere, cylinders, trianglar prism, square prism, rectangular prism, and pentagonal prism
Quick comparison of the listed 3D shapes (key properties, counts, and formulas):
Cube
Base/shape: 6 square faces (all equal).
Faces/edges/vertices: 6 faces, 12 edges, 8 vertices.
Curved surfaces: none.
Volume: V = a^3
Surface area: SA = 6a^2
Rectangular prism (cuboid)
Base/shape: 6 rectangular faces (opposite equal).
Faces/edges/vertices: 6, 12, 8.
Curved surfaces: none.
Volume: V = l·w·h
Surface area: SA = 2(lw + lh + wh)
Square prism
Base/shape: prism with square base (two square bases + 4 rectangles).
Faces/edges/vertices: 6, 12, 8 (same counts as cube); cube is special case when height = side length.
Volume: V = s^2·h
Surface area: SA = 2s^2 + 4s·h
Triangular prism
Base/shape: two congruent triangular bases + 3 rectangular lateral faces.
Faces/edges/vertices: 5 faces, 9 edges, 6 vertices.
Volume: V = (area of triangular base)·length = (1/2·b·h_base)·L
Surface area: SA = 2·(area base) + (perimeter of base)·L
Pentagonal prism
Base/shape: two congruent pentagonal bases + 5 rectangular lateral faces.
Faces/edges/vertices: 7 faces, 15 edges, 10 vertices.
Volume: V = (area of pentagon)·height
Surface area: SA = 2·(area base) + (perimeter base)·height
Cylinder
Base/shape: two circular bases + one curved lateral surface.
Faces/edges/vertices: 2 flat faces + 1 curved surface (no polygonal edges or vertices).
Volume: V = πr^2·h
Surface area: SA = 2πr(r + h)
Cone (right circular cone)
Base/shape: one circular base + one curved surface meeting at an apex.
Faces/edges/vertices: 1 flat face, 1 curved surface, 0 polygonal edges, 1 vertex (apex).
Volume: V = (1/3)πr^2·h
Surface area: SA = πr(r + s) where s = slant height = √(r^2 + h^2)
Sphere
Base/shape: completely curved surface, no faces, edges, or vertices.
Faces/edges/vertices: 0 (all curved).
Volume: V = (4/3)πr^3
Surface area: SA = 4πr^2
Notes:
Prisms: defined by two parallel congruent polygonal bases; lateral faces are rectangles.
Counts for “edges/vertices” above use standard polyhedral definitions (curved solids like cylinders/cones/spheres are not polyhedra).
