# All 3d-shapes Formulas List

## Surface Area of a Triangular Pyramid

#### Formula:

Surface Area (SA) = ((ab) + (3bl)) / 2

Where,

a = Apothem Length
b = Length of Side
l = Slant Height ## Surface Area of a Square Pyramid

#### Formula:

Surface Area = b2 + 2bl

Where,

b = Base
l = Slant Height ## Volume of a Rectangular Hopper

#### Formula:

V = (H / 3) [(X2Y - x2y) / (X - x)]

Where,

V = Volume
H = Height between Bases
X = Length of Upper Rectangular Base
Y = Width of Upper Rectangular Base
x = Length of Lower Rectangular Base
y = Width of Lower Rectangular Base

## Circular Based Tapered Hopper Volume

#### Formula:

v = (π H / 12) [D2 + Dd + d2]

Where,

V = Volume
H = Height between Bases
D = Diameter of the Upper Circular Base
d = Diameter of the Lower Circular Base

## Height of a Cylinder

#### Formula: Height = v / (π × r2)

v = Volume

## Volume of a Frustum of a Regular Pyramid

#### Formula: V = (h/3)×(a+b+√(a×b))

Where,

V = Volume
H = Altitude
A = Lower Base Area
B = Upper Base Area

## Total Surface Area of Elliptical Cylinder

#### Formula: Total Surface Area = (π × (A + B) × h) + (2 × π × A × B)

Where,

t = Total surface area
A= Semi Major Axis
B= Semi Minor Axis
h = Height

## Lateral Surface Area of Elliptical Cylinder

#### Formula: Lateral Surface Area = h × 2 × π × √((1/2) × ((A × A) + (B × B)))

Where,

h = Height
A = Semi Major axis
B = Semi Minor Axis

## Curved Surface Area of Elliptical Cylinder

#### Formula: Curved surface area = π × H × (A + B)

Where,

H = Height
A = Semi-Major Axis
B = Semi-Minor Axis

## Volume of Elliptical Cylinder

#### Formula: Volume (V) = π × A × B × h

Where,

A = Semi-Major Axis
B = Semi-Minor Axis
h = Height

## Surface Area of Conical Cylinder

#### Formula: Surface Area (SA) = (2 × π × r × h) + ((π × r) × (r+ (√(c2 + r2))))+(π × r2)

Where,

h = Cylinder Height
c = Cone Height

## Lateral Surface Area of Conical Cylinder

#### Formula: Lateral Surface Area = π × 2 × r × h

Where,

h = Height

## Volume of a Conical Cylinder

#### Formula: Volume (V) = (π ×r × r × h) + ((1/3) × (π × r × r × c))

Where,

c = Cone Height
h =Cylinder Height

#### Formula:

r = √(3v / πh)

Where,

v = Volume of Cone
h = Height of Cone

## Truncated Pyramid Volume

#### Formula:

V = (H / 3) × (A² + A × B + B²)

Where,

V = Volume of an Incomplete Pyramid
H = Height
A = Base Side
B = Top Side

## Diagonal of a Cube

#### Formula:

d = √3a

Where,

d = Diagonal of Cube
a = Edge of Cube

## Circumference to Volume

#### Formula:

V = C3 / 6 π2

Where,

C = Circumference Sphere
V = Volume of Sphere

## CSA of Cube

#### Formula:

CSA = L2

Where,

CSA = Cross Section Area of Cube
L = Length of Cube

## Total Surface Area and Volume of Box

#### Formula:

a = hw
b = hl
c = wl
SA = 2[a + b + c]
V = hwl

Where,

h = Height of Box
l = Length of Box
w = Width of Box
SA = Total Surface Area of Box
V = Volume of Box

## Base Area of a Triangular Prism

#### Formula:

Base Area = ( 1 / 2 ) × l × b

Where,

l = Triangle Height
b = Base Length

## Surface Area of a Triangular Prism

#### Formula:

Surface Area = ( Base × Height ) + ( ( Side1 + Side2 + Side3 ) × Prism Height )

#### Formula: I = A × √(6) / 6

Where,

A = Edge Length

## Mid Sphere Radius of Octahedron

#### Formula: M = A / 2

Where,

A = Edge Length

## Surface to Volume Ratio Octahedron

#### Formula: S = 3 × √(6) / A

Where,

S = Surface to Volume Ratio
A = Edge Length

## Diagonal of Octahedron

#### Formula: D = √(2) × a

Where,

D = Diagonal
A = Edge Length

## Edge Length of Octahedron

#### Formula: A = √(E/2/√3)

Where,

E = Surface Area
A = Edge Length

## Center of Gravity of Cone

#### Formula:

g = h / 4

Where,

g = Center of Gravity
h = Height of Cone

## Base Area of a Square Pyramid

#### Formula:

b = a²

Where,

b = Base Surface Area
a = Side length

## Volume of a Square Pyramid

#### Formula:

v = (1 / 3) × a² × h

Where,

a = Side Length
h = Height
v = Volume

## Truncated Square Pyramid

#### Formula:

Truncated Height = h (1 - ( b / a ) )
Total Surface Area = a2 + b2 + ( a2 - b2 ) √( 1+ ( 4 h2 / a2 ) )

Where,

a = Base
b = Truncated Base
h = Total Height