Question

help with geometry volume formulas?

Answer 1

Volume Formulas:
s = side
l = length
h = height
w = width
r = radius

Cube
\(V = s^3\)

Rectangular Prism
\(l*w*h\)

Cylinder
\(\pi * r^2 * h\)

Cone
\(\dfrac13 *\pi * r^2 * h\)

Sphere
\(\dfrac43 *\pi * r^3\)

Right Prism
\(Area\; of\; base*h\)

Right Pyramid
\((\dfrac13 * Area\; of\; base) * h\)

Answer 2

Area Formulas:
s = side
l = length
h = height
w = width
r = radius
d = diagonal

Square
\(A = s^2\)

Rectangle
\(A = l*w\)

Parallelogram
\(A = b*h\)

Trapezoid
\(A = \dfrac12 * h * (b_1 + b_2)\)

Triangle
\(A = \dfrac12 * b * h\)

Circle
\(A = \pi * r^2\)

Rhombus
\(A = \dfrac12 * d_1 * d_2\)

Answer 3

Surface Area Formulas:
BA = Base Area
LA = Lateral Area
FA = Area of One Side
n = number of sides
r = radius
h = height
C = Circumference

Cube
\(SA = 6*s^2\)

Prism
\(SA = 2*BA + LA\)

Pyramid
\(SA = BA + LA\)

Regular Polyhedron
\(SA = FA * n\)

Sphere
\(SA = 4*\pi*r^2\)

Cylinder
\(SA = 2\pi r^2 + 2r\pi h\)

Answer 4

Yay! It's all still in my notebook! :D

Answer 5

Lateral Area Formulas:
\(\it{l}\) = Slant Height
P = Perimeter of Base
C = Circumference of Base (Circles Only)
h = Height
r = Radius

Right Prism
\(LA = Ph\)

Right Cylinder
\(LA = Ch\)
or
\(LA = 2\pi r h\)

Regular Pyramid
\(LA = \dfrac12 P\it{l}\)

Right Cone
\(LA = \dfrac 12 C\it{l}\)
or
\(LA = \pi r\it{l}\)

Cube
\(LA = 4s^2\)

Rectangular Prism
\(LA = 2h(l+w)\)

Answer 6

Other Important Formulas:

Pythagorean Theorem
\(a^2 + b^2 = c^2\)

Distance Formula
\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint Formula
\(\dfrac{x_1+x_2}2,\dfrac{y_1+y_2}2\)

Quadratic Formula
\(x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Answer 7

Exponent Rules:

\(x^m * x^n = x^{m+n}\)

\(\dfrac{x^m}{x^n} = x^{m-n}\)

\(b^{-n} = \dfrac{1}{b^n}\)

\( \dfrac{1}{b^{-n}} = b^{n}\)

\((x{^m})^n\) = \(x^{mn}\)

\((xy)^m = x^my^m\)

\((\dfrac{ax}{by}){{^{^{^{^m}}}}} = \dfrac{a^mx^m}{b^my^m}\)

\(x^0 = 1\)