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By Automathic

Tags: Volume, Cylinder, Pi, Radius, Height

0

Posted: 2013-09-16
Volume of a Cylinder
Volume of a Cylinder
$$$V = \pi r^2 h$$$

A cylinder with a radius of r and height h units has a volume of V cubic units. One of those simple formulas that tends to be forgotten.



By PiThagoras

Tags: Volume, Trangle, Prism, Height, Base, Length, (1/2...

0

Posted: 2013-09-16
Volume of a Triangular Prism
Volume of a Triangular Prism
$$$V = {1 \over 2} B * H * L$$$

A simple adaptation of the Area of a Triangle formula (http://automathic.org/114) to calculate the volume (V) of a Triangular Prism (https://en.wikipedia.org/wiki/Triangular_prism) with a base of B, height of H, and length of L.



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By PiThagoras

Tags: Circumference, Circle, pi, radius, diameter

0

Posted: 2013-09-16
Circumference of a Circle
Circumference of a Circle
$$$C = 2 \pi r = \pi d$$$

"Circumference is the linear distance around the outside of a closed curve or circular object." It can be calculated using the above, where C is the circumference using either the radius (r) or the diameter (d), depending on what's convenient.

More info can be found here: https://en.wikipedia.org/wiki/Circumference



By Isa McKenty

Tags: Circle, Area, Radius, Root, Pi, Diameter, Circumference

0

Posted: 2013-11-11
Radius of a Circle from its Area
Radius of a Circle from its Area
$$$r = \sqrt{A \over \pi}$$$

If you need to find the Radius ($$r$$) of a circle, and only have the Area ($$A$$) to work with, you can use this handy formula.

If you have the Circumference, use this formula: www.automathic.org/152_radius-of-a-circle



By Automathic

Tags: Algebra, Radicals, Exponents, Algebraic, Arithmetic,...

0

Posted: 2013-11-12
The Rules of Algebra
The Rules of Algebra

Algebrarules.com is Automathic's latest project, where you can find the rules of algebra for Arithmetic, Exponents, and Radicals — with more to come. It's The Rules of Algebra, Sweet 'n Simple.



By PiThagoras

Tags: Area, Kite, Diagonal, Diagonals Method, a = d1*d2/2

0

Posted: 2014-02-04
Area of a Kite
Area of a Kite
$$$Area = { d_1 * d_2 \over 2}$$$

If you know the lengths of the diagonals — d1 and d2 — of a kite, finding the area is simple with the formula above.

Otherwise, you can use this method:

$$$ Area = a * b * sin(c) $$$

Where $$a, b$$ are the lengths of two unequal sides, and $$c$$ is the angle between them ($$sin$$ being the trignometric function sine https://en.wikipedia.org/wiki/Sine)



By Isa McKenty

Tags: Ellipse, Area, Pi, Major Semi-axis, minor semi-axis,...

0

Posted: 2014-02-05
Area of an Ellipse
Area of an Ellipse
$$$Area = \pi ab$$$

The area of an ellipse can be found when you know the measures of the major and minor semi-axis, $$a$$ and $$b$$.

Image courtesy of Wikimedia commons, licensed as creative commons.



By Isa McKenty

Tags: Sphere, Surface Area, Area, Pi, Globe, 4\pir^2

0

Posted: 2014-02-09
Surface Area of a Sphere
Surface Area of a Sphere
$$$4 \pi r^2$$$

The surface area of a sphere can be found with the above formula, where $$r$$ is the radius. It can also be notated as $$$\pi d^2$$$ Where $$d$$ is the diameter.



By PiThagoras

Tags: improper fraction, mixed number, remainder, quotient,...

0

Posted: 2014-09-05
Improper Fraction to Mixed Number
Improper Fraction to Mixed Number
$$${a \over b} = quotient + {remainder \over divisor}$$$

To convert an Improper Fraction to a Mixed Number:

  • • Divide the numerator by the denominator (with long division)
  • • The result (quotient) of the division becomes the who part of the mixed number
  • • The fractional part of the mixed number is the remainder over the original denominator

To convert the other way, use this formula: http://automathic.org/158_convert-a-mixed-number-to-an-improper-fraction



By Nathaniel

Tags: Electronics, Inductors

0

Posted: 2016-08-22
Inductors in series
Inductors in series
$$${L_t} = {L_1} + {L_2} + {L_3}$$$

Formula for inductors in series where L1 is the inductance of the first inductor, L2 is the inductance of the second inductor, L3 is the inductance of the third inductor, and L t is the total of all the inductors in series



By Nathaniel

Tags: Electronics, Capacitors

0

Posted: 2016-08-22
Capacitors in parallel
Capacitors in parallel
$$${C_t} = {C_1} + {C_2} + {C_3}$$$

Formula for capacitors in parallel where C1 is the capacitance of the first capacitor, C2 is the capacitance of the second capacitor, C3 is the capacitance of the third capacitor, and C t is the total of all the capacitors in parallel



By Nathaniel

Tags: Electronics, Capacitors

0

Posted: 2016-08-22
Capacitors in series
Capacitors in series
$$${1 \over C_t} = {1 \over C_1} + {1 \over C_2} + {1 \over C_3}$$$

Formula for capacitors in series where C1 is the capacitance of the first capacitor, C2 is the capacitance of the second capacitor, C3 is the capacitance of the third capacitor, and C t is the total of all the capacitors in series



By PiThagoras

Tags: Hero's, Herons, Triangle, Height, Area, Base, Theorem

-1

Posted: 2013-01-17
Hero's Formula
Hero's Formula
$$$s= {a+b+c \over 2} \\ Area = s \sqrt{s(s-a)+s(s-b)+s(s-c)}$$$

Hero's Theorem is used to determine the Area of a Triangle with the side lengths a b c when you do not have the Height and Base measurements.



By Automathic

Tags: Pi, Circumference, Diameter, Circle

-1

Posted: 2013-03-07
Determining The Value of Pi
Determining The Value of Pi
$$$\pi = {C \over d}$$$

The constant Pi is equal to ~ (3.141592653589397....), and represents the ratio between a circle's circumference (C) and diameter (d) .



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