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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Mathematics is the most important tool of science. The quest to understand the world and the universe using mathematics is as old as civilisation, and has led to the science and technology of today. Learn about the techniques and history of mathematics on ScienceLibrary.info.

1873 - 1916

Karl Schwarzschild was a German astronomer and physicist, and a pioneer of the field of astrophysics. He solved Einstein's field equations while serving as an artillery office on the Eastern Front, during World War One.

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