Pi facts
What is PI?
Ratio of circumference to diameter of a circle.
What is the equation for the area of a circle?
A=πr^2 (Area= PI*Radius-squared)
How do you convert Radians to Degrees?
Radians= π/180*degrees
(number of degrees*PI over 180)
What is π in degrees?(Pi)
180 degrees
If the diameter of a circle is 10cm, what is its circumference in regards to PI?
C=2πR, R=1/2 diameter
so C= 2π(5) = 10π
When was PI first used?
1706
What is the equation for the volume of a Sphere?
4πr^3/3 or Four Pi Times Radius Cubed Divided by Three
What is Cos at π/3 radians on the unit circle?
Square-root of 3 over 2
What is 360 degrees in Radians?
2π or Two Pi
What is the circumference of a hula hoop that has a radius of 5 in terms of Pi?
10π or Ten Pi
When is National PI Day? Why?
March 14th
(because march is the 3rd month, on the 14th day it makes 3.14, the first most commonly used digits of PI)
What shapes include Pi to find Surface Area? (List All)
Cylinder, Cone and Sphere
What Two Special Triangles are used to tell the points on the Unit Circle?
30,60, and 90 Right Triangle, and the 45, 45, 90 Right Triangle
What is 30 degrees in Radians?
π/6 (PI over six)
How much wood would a woodchuck chuck, if a wood chuck could chuck wood?
If a woodchuck could chuck wood, then a woodchuck would chuck as much wood as a woodchuck could chuck wood.
What kind of number is Pi?
(Hint:What are people who take Calculus?)
Irrational
If you had a cylindrical cup of water, what equation would you use to find the volume of water in the cup?
V=πR^2*h (PI* radius squared*height)
When were the concepts of angles and trigonometry applied to a circle, creating a primitive Unit Circle?
Between 90-168 AD
(Accepting 20 year error)
What is π/4 in degrees?
45 degrees
If X=2π/3, Solve:
y=1/3πsin(x)+5π/2
sin(2π/3)= square-root of 3 over 2
so Y= ((square-root of 3 over 2) plus 15π) all over 6π
What letter of the Greek alphabet is PI?
(the first letter, 2nd, 3rd, 4th...?)
The 19th Letter of the Greek Alphabet
Name three real-life field applications of PI
Building and Construction, Quantum physics, Communications, Music theory, Medical procedures, Air travel, and Space flight.
Who applied the concepts of angles and trigonometry to a circle, creating a primitive Unit Circle?
Claudius Ptolemy
(will accept a close-to last name or mispronunciation)
What is 315 degrees in radians?
7π/4 or Seven Pi divided by 4
You are given an ice cream cone. You want to see how much ice cream the waffle cone can hold to the rim. You know the height is 3 and the diameter is 6. What is the volume?
18π or Eighteen Pi