Mathematical Formulas for Industrial and Mechanical Engineering

4.1 Plane Figures—Perimeter (P), Circumference (C),

and Area (A)

Rectangle Parallelogram Trapezoid Triangle Circle

P 5 2l 1 2wC5 2πr

A 5 lw A 5 bh A 5 (1/2)(a 1 b)hA5 (1/2)bh A 5 πr

2

w

l

h

b

h

a

b

h

b

r

4.2 Solid Figures—Surface Area (S) and Volume (V)

Rectangular Solid Circular Cylinder Circular Cone Sphere

S 5 2wl 1 2hl 1 2wh S 5 2πr

2

1 2πrh S 5 πr

2

1 πr

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðr

2

1 h

2

Þ

p

S 5 4πr

2

V 5 lwh V 5 πr

2

hV5 (1/3)πr

2

h V 5 (4/3)πr

3

h

w

l

r

h

h

r

r

r

4.3 Right Triangle

A

C

a

b

c

α

β

B

c

2

5 a

2

1 b

2

or c 5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a

2

1 b

2

p

(Pythagorean Theorem)

α 1 β 5 90



54 Mathematical Formulas for Industrial and Mechanical Engineering