Geometry Quick Guide 5: 3D Shape Formulas
Name Date
GEOMETRY QUICK GUIDE 5: 3D SHAPE FORMULAS
3D SHAPES CUBE CUBOID (RECTANGULAR PRISM) All 3d shapes can be described in terms of Volume = s3 Volume = ℓ x w x h their faces, vertices and edges. Surface area = 6s2 Surface area = 2ℓh + 2ℓw + 2wh Face - a flat or curved surface where s is the length of one side where ℓ = length, w = width, h = height Edge - line where 2 faces meet Vertex - point where 3 or more edges meet h face s edge
ℓ w vertex
PYRAMIDS REGULAR TETRAHEDRON SQUARE PYRAMID 3 1 2 Volume of a general pyramid = 1/3 Ah Volume = b /6√2 Volume = /3 s h where A = base area and h = height Surface area = √3b2 Surface area = s2 + 2sh
b h h
A b s PRISMS TRIANGULAR PRISM Volume of any prism = Ah Volume = A ℓ or ½ bhℓ Surface area = bh + 2ℓs + ℓb Surface area of a closed prism = 2A + (h x p) s where A = base area, h = height, p = base perimeter
h A h h ℓ
b A A p p
SPHERES RIGHT CYLINDER RIGHT CIRCULAR CONE Volume = 4/3 пr3 Volume = пr2h Volume = 1/3 пr2h Surface area = 4пr2 Surface area = 2пr (r + h) Surface area = пr (r + s)
r
h r h s r
Name Date
GEOMETRY QUICK GUIDE 5: 3D SHAPE FORMULAS
3D SHAPES CUBE CUBOID (RECTANGULAR PRISM) All 3d shapes can be described in terms of Volume = s3 Volume = ℓ x w x h their faces, vertices and edges. Surface area = 6s2 Surface area = 2ℓh + 2ℓw + 2wh • Face - a flat or curved surface where s is the length of one side where ℓ = length, w = width, h = height • Edge - line where 2 faces meet • Vertex - point where 3 or more edges meet s h face edge
ℓ w vertex
PYRAMIDS REGULAR TETRAHEDRON SQUARE PYRAMID 3 1 2 Volume of a general pyramid = 1/3 Ah Volume = b /6√2 Volume = /3 s h where A = base area and h = height Surface area = √3b2 Surface area = s2 + 2sh
b h h
A
b s
PRISMS TRIANGULAR PRISM Volume of any prism = Ah Volume = A ℓ or ½ bhℓ Surface area = bh + 2ℓs + ℓb Surface area of a closed prism = 2A + (h x p) s where A = base area, h = height, p = base perimeter
h A h h ℓ b A A p p
SPHERES RIGHT CYLINDER RIGHT CIRCULAR CONE Volume = 4/3 пr3 Volume = пr2h Volume = 1/3 пr2h Surface area = 4пr2 Surface area = 2пr (r + h) Surface area = пr (r + s)
r
h r h s r