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Common Formulas

CIRCUMFERENCE

Circle:

C = πd, in which π is 3.1416 and d the diameter.

AREA

Triangle:

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

Square:

A = a², 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 = 1.720a², in which a is one of the sides.

Regular hexagon:

A = 2.598a², in which a is one of the sides.

Regular octagon:

A = 4.828a², in which a is one of the sides.

Circle:

A = πr², in which π is 3.1416 and r the radius.

VOLUME

Cube:

V = a³, 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 = πr²h, in which π is 3.1416, r the radius of the base, and h the height.

Cone:

V = (πr²h)/3, in which π is 3.1416, r theradius of the base, and h the height.

Sphere:

V = (4πr³)/3, in which π 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 Kelvins:

T_K = T_C + 273.15

Mean and Median

The arithmetic mean, also called the average, of a series of quantities is obtained by finding the sum of the quantities and dividing it by the number of quantities. In the series 1, 3, 5, 18, 19, 20, 25, the mean or average is 13—in other words, 91 divided by 7.

The median of a series is that point which so divides it that half the quantities are on one side, half on the other. In the above series, the median is 18.

The median often better expresses the common-run, since it is not, as is the mean, affected by an excessively high or low figure. In the series 1, 3, 4, 7, 55, the median of 4 is a truer expression of the common-run than is the mean of 14.

MISCELLANEOUS

Distance in feet traveled by falling body:

d = 16t², 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 = mc², 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: (c² = 9 × 10²⁰)