# Common Formulas

### Circumference

**Circle:** C = Î d, in which Î is 3.1416 and *d* the diameter.

### Area

**Triangle:** A = (ab)/2 , in which *a* is the base and *b* the height.

**Square:**** **A = a^{2}, in which *a* is one of the sides.

**Rectangle: **** **A = ab, in which *a* is the base and *b* the height.

**Trapezoid: **** **A = (h(a + b))/2, in which *h* is the height, *a* the longer parallel side, and *b* the shorter.

**Regular pentagon: **** **A = 1.720a^{2}, in which *a* is one of the sides.

**Regular hexagon: **** **A = 2.598a^{2}, in which *a* is one of the sides.

**Regular octagon: **** **A = 4.828a^{2}, in which *a* is one of the sides.

**Circle: **** **A = Î r^{2}, in which Î is 3.1416 and *r* the radius.

### Volume

**Cube:** V = a^{3}, in which a is one of the edges.

**Rectangular prism: **** **V = abc, in which *a* is the length, *b* is the width, and *c* the depth.

**Pyramid: **** **V = (Ah)/3, in which *A* is the area of the base and *h* the height.

**Cylinder: **** **V = Î r^{2}h, in which Î is 3.1416, *r* the radius of the base, and *h* the height.

**Cone: **** **V = (Î r^{2}h)/3, in which Î is 3.1416, *r* theradius of the base, and *h* the height.

**Sphere: **** **V = (Î 4r^{3})/3, in which Î is 3.1416 and *r* the radius.

### Temperature Scales

**Degrees Fahrenheit to Degrees Celsius:** T_{C} = ^{5}/9 (T_{F}, 32)

**Degrees Celsius to Degrees Fahrenheit: **** **T_{F} = ^{9}/5 T_{C} + 32

**Degrees Celsius to Kelvin: **** **T_{K} = T_{C} + 273.15

### Miscellaneous

**Distance in feet traveled by falling body:** d = 16t^{2}, in which *t* is the time in seconds.

**Speed of sound in feet per second through any given temperature of air: **** **take the square root of (273 + t), in which *t* is the temperature Centigrade, multiply it by 1087, and divide the result by 16.52.

**Cost in cents of operation of electrical device: **** **C = (Wtc)/1000, in which *W* is the number of watts,*t* the time in hours, and *c* the cost in cents per kilowatt-hour.

**Conversion of matter into energy (Einstein’s Theorem): **** **E = mc^{2}, in which *E* is the energy in ergs, *m* the mass of the matter in grams, and *c* the speed of light in centimeters per second: (c^{2} = 9 Ã— 10^{20})

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