OAR Formulas
Volume of a cone - answerV=(1/3)πr²h
Area of a triangle - answerA=(1/2)bh
Area of a circle - answerA=πr²
Volume of a regular prism - answerV=lwh
Volume of a cube - answerV=s³
Volume of a sphere - answerV=(4/3)πr³
Volume of cynlinder - answerV=πr²h
Outlier - answer1.5 x IQR above or below upper or lower bound
Z-score - answerz = (x - mean) / standard deviation
Area of a trapezoid - answerA=1/2h(b1+b2)
Distance formula - answerd = √[( x₂ - x₁)² + (y₂ - y₁)²]
Circumpherence of circle - answerC=2πr
Arc length - answerarc = angle/360 x 2πr
Scale a polygon by "k" - answer(x,y) ---> (kx,ky)
Area of a sphere - answerA=4πr²
Velocity - answerV = distance(including direction) / time
Acceleration - answerA = change in velocity / time
Force - answerF = mass x acceleration
Momentum - answerM = mass x velocity
Work - answerW = force x distance
(newton meters)
Potential energy - answerPE = mass x acceleration of gravity x distance(y)
, (newton meters)
Kinetic energy - answerKE=(1/2)mv²
(newton meters) -- v² = (2 x work output) / mass
Energy - answerEnergy = Work = force x distance
Work (fluids) - answerWork = pressure x piston area x displacement
or
Work = pressure x change in volume
Pressure - answerP = F(force) / A(area)
P = weight of liquid x distance
P = density of liquid x depth x acceleration of gravity
Flow rate - answerQ = v x A
- For a given flow rate, a smaller pipe requires a higher velocity
Effort (lever) - answerF = R(load) x [L2(lever arm btwn. fulcrum and load) / L1 (lever arm
btwn. fulcrum and force/effort)]
Effort (wheels/axles) - answerF = L(load) x [r(radius of axle) / R (radius of wheel)]
Speed of gears - answer(Revolutions of gear B / Revolutions of gear A) = (Number of
teeth gear A / Number of teeth gear B)
Force (ramp) - answerF = (H/D) x W(weight)
Mechanical advantage of a car jack - answerF = L(length of threaded portion) x [p(pitch)
/ 2πR(length of lever)]
Revolution - answerR = 2π radians
Projectile motion (no time) - answerd = [v(f)² - v(i)²] / 2a
v(f)² = v(i)² + 2ad
Projectile motion (no distance) - answerv(f) = v(i) + at
Projectile motion (no acceleration) - answerd = [(v(i) + v(f)) / 2] x t
Projectile motion (no final velocity) - answerd = v(i)t + (1/2)at²
Density - answerd = mass / volume
Liters ---> meters cubed (conversion) - answer1,000L = 1m³
Volume of a cone - answerV=(1/3)πr²h
Area of a triangle - answerA=(1/2)bh
Area of a circle - answerA=πr²
Volume of a regular prism - answerV=lwh
Volume of a cube - answerV=s³
Volume of a sphere - answerV=(4/3)πr³
Volume of cynlinder - answerV=πr²h
Outlier - answer1.5 x IQR above or below upper or lower bound
Z-score - answerz = (x - mean) / standard deviation
Area of a trapezoid - answerA=1/2h(b1+b2)
Distance formula - answerd = √[( x₂ - x₁)² + (y₂ - y₁)²]
Circumpherence of circle - answerC=2πr
Arc length - answerarc = angle/360 x 2πr
Scale a polygon by "k" - answer(x,y) ---> (kx,ky)
Area of a sphere - answerA=4πr²
Velocity - answerV = distance(including direction) / time
Acceleration - answerA = change in velocity / time
Force - answerF = mass x acceleration
Momentum - answerM = mass x velocity
Work - answerW = force x distance
(newton meters)
Potential energy - answerPE = mass x acceleration of gravity x distance(y)
, (newton meters)
Kinetic energy - answerKE=(1/2)mv²
(newton meters) -- v² = (2 x work output) / mass
Energy - answerEnergy = Work = force x distance
Work (fluids) - answerWork = pressure x piston area x displacement
or
Work = pressure x change in volume
Pressure - answerP = F(force) / A(area)
P = weight of liquid x distance
P = density of liquid x depth x acceleration of gravity
Flow rate - answerQ = v x A
- For a given flow rate, a smaller pipe requires a higher velocity
Effort (lever) - answerF = R(load) x [L2(lever arm btwn. fulcrum and load) / L1 (lever arm
btwn. fulcrum and force/effort)]
Effort (wheels/axles) - answerF = L(load) x [r(radius of axle) / R (radius of wheel)]
Speed of gears - answer(Revolutions of gear B / Revolutions of gear A) = (Number of
teeth gear A / Number of teeth gear B)
Force (ramp) - answerF = (H/D) x W(weight)
Mechanical advantage of a car jack - answerF = L(length of threaded portion) x [p(pitch)
/ 2πR(length of lever)]
Revolution - answerR = 2π radians
Projectile motion (no time) - answerd = [v(f)² - v(i)²] / 2a
v(f)² = v(i)² + 2ad
Projectile motion (no distance) - answerv(f) = v(i) + at
Projectile motion (no acceleration) - answerd = [(v(i) + v(f)) / 2] x t
Projectile motion (no final velocity) - answerd = v(i)t + (1/2)at²
Density - answerd = mass / volume
Liters ---> meters cubed (conversion) - answer1,000L = 1m³
