GEOMETRY INVOLVING PI
PI DEFINITION & HISTORY
PI TRIVIA
PRE-CALCULUS INVOLVING PI
SAT INVOLVING PI
100
What is the area of the circle with radius 3? a. 9π b.3π c.6π d.π
a. 9π
100
Pi is an irrational number. What does that really mean? a. Its digits cannot be rationed out evenly b. Nobody with sound judgement has anything to do with it c. it is a real number, but can't be expressed as a ratio of two integers
c. it is a real number, but can't be expressed as a ratio of two integers
100
Pi is transcendental. What does this mean, in mathematics? a. It is equal to the ratio of two integers b. Its square root is imaginary c. It cannot be expressed as an integer, or as a root or quotient of integers d. It was Ralph Waldo Emerson's favorite number.
c. It cannot be expressed as an integer, or as a root or quotient of integers
100
What is cos(π)? a. -1 b. 1 c. 0 d. Undefined
a. -1
100
You walk around a circle which has a diameter of 300m. How far have you walked? A. 471m B. 900m C. 942m D. 1,200m
C. 942m
200
If a diameter of a circle is 142.8 mm, what is its radius? a. 71.4 mm b. 45.48 mm c.3.14mm d.1.69mm
a. 71.4
200
What is the "formal" definition of pi? a. the surface area of a sphere of diameter 22/7 b. 3.1415926 c. the radius of a circle d. a delicious dessert e. the ratio of a circle's circumference to its diameter
e. the ratio of a circle's circumference to its diameter
200
1f you calculated the circumference of a circle the size of the known universe, requiring that the answer be accurate to within the radius of one proton, how many decimal places of pi would you need to use? (i.e., 3.14, or 3.1415, or 3.1415926, etc.)? a. two million b. 39 c. 48,000 d. 6 billion
b. 39
200
What is sin(4π/3) in radian form? a. -√3 over 2 b. √3 over 2 c. √2 over 2 d. √3
a. -√3 over 2
200
Imagine if you wrapped a rope tightly around the earth at the equator. How much longer would you have to make the rope if you wanted it to be exactly one foot above the surface all the way around? A. 2 pi feet B. 2 pi r feet, where r is the radius of the earth C. pi r2 feet
A. 2 pi feet
300
Suppose a water tank in the shape of a right circular cylinder is thirty feet long and eight feet in diameter. How much sheet metal was used in its construction? Hint:SA=2(π)rh
272π ft^2
300
Who, in 1706, first gave the Greek letter "pi" its current mathematical definition? a. Albert Einstein b. William Jones c. Attila the Hun d. Archimedes e. Napoleon Bonaparte
b. William Jones
300
People tried for centuries to "square the circle". What were they trying to do? a. Construct a square that perfectly circumscribes (surrounds) a given circle b. Determine the value of pi squared c. Multiply a circle by itself d. Use a straightedge and compass to construct a square exactly equal in area to a given circle e. Alter a recipe intended for a round pan so that it would fit exactly into a square pan
d. Use a straightedge and compass to construct a square exactly equal in area to a given circle
300
Find sin(x) and tan(x) if cos(pi/2 - x) = - 3/5 and sin(x + pi/2) = 4/5? a. sin(x)= -3/5, tan(x) = -3/4 b. sin(x)= 4/5, tan(x)= -4/3 c. sin(x)= -3/5, tan(x)+ 4/5 d. Not enough informaton
a. sin(x)= -3/5, tan(x) = -3/4
300
"DAILY DOUBLE" Which of the following gives the best estimate for pi? (You may use your calculator) A. 3.14 B. 22/7 C. √(10) D.31^(1/3)
D.31^(1/3)
400
Find the diameter of a circle with a circumference of 21.98 meters.
7
400
What is the earliest known reference to pi in history? a. The Rosetta Stone, approx. 200 BC b. The Bible c. An Egyptian papyrus scroll, written approx. 1650 BC by Ahmes the Scribe d. Euclid's Elements, written in the 3rd century BC
c. An Egyptian papyrus scroll, written approx. 1650 BC by Ahmes the Scribe
400
Some people became mentally deranged when trying to "square the circle". What was this illness named? a. Impossibilius Fittus b. Morbus Cyclometricus c. Repetitionatis Decimalus
b. Morbus Cyclometricus
400
What is the exact value of [ tan (25 °)+ tan (50 ° ] / [ 1 - tan( 25 °) tan(50 °) ]? a. √3 +2 b. √3 - 2 c. √6- 10 d. Not enough information
a.√3 +2
400
Which of the following statement(s) are correct? 1. pi is the ratio of Circumference to the Diameter of a Circle. 2. pi=3.14 3. pi=22/7 4. pi is a irrational number A.1&4 B.2&3 C.4 only D.1&2
A. 1&4
500
Triangle ABC is a triangle inscribed inside the circle of center O and radius r = 10 cm. Find the lengths of AB and CB so that the area of the shaded region is twice the area of the triangle. O bisects AC, and AC is the diameter. BC is the arc of the circle.
AB=19.24, CB=5.45 or AB=5.45, CB=19.24
500
"DOUBLE JEOPARDY" Are pi's digits periodic? In other words, do the digits ever repeat themselves in any pattern? a. Yes. The digits repeat themselves every 6,000,000 decimal places b. No. Every periodic number is rational, but pi is irrational c. Yes. Every infinitely long number repeats itself d. Perhaps. Not enough digits of pi have been calculated to know yet
b. No. Every periodic number is rational, but pi is irrational
500
Among the digits of pi currently known, the concentration of each of the digits 0-9 are pretty close to equal. However, in the first 30 places of pi's decimal expansion, which digit is completely missing? a. 7 b. 2 c. 0 d. 8
c. 0
500
"DOUBLE JEOPARDY" A ferris wheel with a radius of 25 meters makes one rotation every 36 seconds. At the bottom of the ride, the passenger is 1 meter above the ground. What is the height, above the ground of the passenger? Determine h as a function of time if h=51 meters and t=0 Find height h after 45 seconds. a.25cos((π/18)t) +26; 26 m b.25sin((π/18)t) +26, 30 m c.25tan(π/18)t) + 26, 0 m d. Not enough information given
a.25cos((π/18)t) +26; 26 m
500
What is the percent error in using 3.14 as an approximation for pi? (No Calculator Allowed) A. 0.0015% B. 0.005% C.0.05% D.5%
C.0.05%
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