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Mathematical Formulae

Area, Surface Area and Volume Formulae

 

Shape
Area Formulas
Square with sides of length a

square

Area = a^2
rectangle with sides of lengths a and b

rectangle 

Area = a*b
circle of radius r

circle

Area = pi*r^2
Triangle with sides of lengths a, b and c. b is the longest side. C is the angle opposite the side of length c. h is the perpendicular distance from b to the angle opposite b.

triangle

Area = (1/2)*b*h
A = (1/2)*a*b*sinC
Area = sqrt(s(s-a)(s-b)(s-c))   where  s=(a+b+c)/2
Trapezium with parallel sides of lengths a and b and height h.

trapezium

A = (h/2)*(a+b)
ellipse. Shortest distance from center is b. Longest distance from center is a.

ellipse

A = pi*a*b

 

Shape
Surface Area Formulas

cube

Cube with sides of length a.
Surface Area = 6*a^3

rectangular prism

Rectangular prism with sides of length a, b c.
SA = 2ab+2bc+2ac

cylinder

Cylinder, radius r, height h.
SA = 2*pi*r^2 + 2*pi*r*h

sphere

Sphere radius r
SA = 4*pi*r^2

 

Shape
Volume Formulas

cube

Cube with sides of length a.
V=a^3

rectangular prism

Rectangular prism with sides of length a, b c.
V=abc

cylinder

Cylinder, radius r, height h.
V=pi*r^2*h

cone

Cone, radius r, height h
V=1/3*pi*r^2*h

sphere

Sphere radius r
V=4/3*pi*r^3

ellipsoid

Ellipsoid, perpendicular shortest distances from center are a, b, c
V=4/3*pi*a*b*c

 


Mathematical Formulae Index

 

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