Cube: $A = L^3$

$A = 4πr^2$

$A = B + {PL}/2$, where B is the area of the base, P is the perimeter of the base, and L is the height of the slant $L= √{{h^2+r^2}}$ where h is the pyramid height and r is the inradius of the base.

$A = πr(r + l)$, where r is the radius of the base, and l is the lateral length, given by $l = √{r^2 + h^2}$, where h is the height of the cone.

$A = πd(r + h)$, where d is the diameter of the base, r the radius of the base and h the height of the cylinder.

The length of an arc = $({θ}/{2π})(2πr) = rθ$

This formula assumes the angle is given in radians.

The area of a sector = $({θ}/{2π})(πr^2)={θr^2}/2$

where r the radius of the circle, and the sector subtends the central angle θ.

Length of chord: $2r$sin$(θ/2)$, where the chord is subtended by central angle $θ$ of a circle with radius $r$.

Sagitta = perpendicular line from the centre of a chord to the circumference of a circle. The length of the sagitta is $r - r$cos$C/2$, where $r$ is the radius of the circle and C the angle at the centre subtended by the chord.

The area of a circle segment is:

$A_{seg} = 1/2(L_ar-L_c(r-h))=1/2r^2(θ-sin(θ))$

where $θ$ is the central angle in radians, $r$ is the radius, $L_a$ is the length of the arc, and $L_c$ is the length of the chord.

A radian is the size of the angle subtended by an arc the same length as the radius of the circle.

Since the circumference of a circle is 2πr, there are 2π radians in 360°.

One radian is equal to ${360°}/{2π} = 57.2957795°$. Since π is irrational, the radian cannot be expressed exactly in degrees.

$V = L^3$

$V = 4/3πr^3$

$V = 1/3BH$, where B is the area of the base, and H is the height, measured perpendicularly from the base to the apex.

$V = πr^2H$, where H is the height and r is the radius of the base circle.

$V = 1/3 π r^2 h$

where V is the volume, r is the radius of the base circle, and h is the height of the cone.

$x^2+y^2=r^2$

${x/a}^2+{y/b}^2=r^2$, where $a$ and $b$ are the major and minor axes.

${x/a}^2+{y/b}^2= $sin$^2θ + $cos$^2θ$, where $θ$ is the angle to a point on the ellipse from the centre, and x and y are the Cartesian coordinates of the point, where $x=0$ and $y=0$ is the centre.

$ax^2+bx+c$

${x/a}^2-{y/b}^2=1$

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Physics is the science of the very small and the very large. Learn about Isaac Newton, who gave us the laws of motion and optics, and Albert Einstein, who explained the relativity of all things, as well as catch up on all the latest news about Physics, on ScienceLibrary.info.

1867 - 1934

Marie Curie, née Skłodowska, was a Polish physcist and chemist, fêted as one of the most brilliant minds ever. Although her life was marked by regular tragedy and oppression, as a Pole and as a woman, she triumphed in the end, gaining a remarkable two Nobel Prizes.

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