Pi Day (March 14) Meeting
(Multiple Topics)
Topic
There are a variety of math topics covered in the problems used for this meeting. However,
each problem uses in some way.
Materials Needed
♦ Copies of the set of problems provided (available for download from www.mathcounts.org/
MCP0708Resources)
Meeting Plan
March 14 (3/14) is Pi (3.14…) Day! We encourage you to check out the many Web sites that
include activities, songs, games, etc. related to Pi Day that you can use with your math club or
with your entire school. One such site is www.piday.org, but there are many, many more.
MATHCOUNTS materials have a wealth of problems that use in their solutions, and we
encourage you to find your favorites in Volumes I and II of the 2007-2008 MATHCOUNTS
School Handbook. We have provided a few problems below, too, that you can use during your
Pi Day activities. You can download a more student-friendly copy of these problems in larger
font from www.mathcounts.org/MCP0708Resources.
We hope you find these problems to be as easy as 3.141592653589793238462643383…!
(If you’re in need of a great prize for your Pi Day activities, check out the MATHCOUNTS Store
at www.mathcounts.org where we have “It’s As Easy As 3.141592653589793238462643383….”
T-shirts available.)
1. When is written out in decimal form, what percent of the first 10 digits to the right of the decimal point are 5s?
2. Math people often use the fraction 22/7 to represent the value of . If we had to use the common fraction x/22 to
represent , what integer-value of x would give us the closest approximation?
3. How many positive integers are less than 10?
4. If Tony memorized 85 digits of , and he recited them in exactly 18 seconds, then he recited them at the average
rate of how many digits per second? Express your answer to the nearest whole number.
5. A particular circle’s circumference is 4 inches, and its area is 4 square inches. What is the radius of the circle, in
inches?
6. Pam Piper prepared a plum pie in a circular pan with a diameter of 9 inches. If the pie piece that Polly Peters
purchased from Pam Piper was square inches on the bottom, what percent of Pam Piper’s prepared plum pie did
Polly Peters purchase? Express your answer to the nearest whole number.
**The following problems are all from the 2007-2008 MATHCOUNTS School Handbook, Volume I. **
7. What is the area, in square units, of the circle that is centered at the origin and is tangent to the line y = 7?
Express your answer in terms of .
8. Four congruent quarter-circles are drawn inside a square of side length 4 cm, as shown. What is the
area of the shaded portion of the square region, in sq cm? Express your answer in terms of .
2007-2008 MATHCOUNTS Club Resource Guide
43
9. This square has an area of 49 square centimeters. What is the area of the inscribed circle, in sq cm?
Express your answer as a decimal to the nearest tenth.
10. The formula for the total surface area of a cylinder is SA = 2r 2 + 2rh, where r is the radius and h is the height.
A particular solid right cylinder of radius 2 feet has a total surface area of 12 square feet. What is the height of the
cylinder, in feet?
Answers: 30%; 69; 31 integers; 5 digits per second; 2 inches; 5%; 49 square units; 4 sq cm; 38.5 sq cm;
1 foot
If you have a successful Pi Day with your club or at your school, we encourage you to
take pictures and share the photos, as well as your Pi Day plans, with us so that we
can then share them with the MATHCOUNTS community. Please e-mail them to info@
mathcounts.org with the subject line “MATHCOUNTS Club Program.” Thank you in advance!
44
2007-2008 MATHCOUNTS Club Resource Guide
 Pi Day 
PI
Problem Set
PI
1. When Π is written out in decimal form, what percent of the first 10 digits to the
right of the decimal point are 5s?
2. Math people often use the fraction 22/7 to represent the value of Π. If we had to
use the common fraction x/22 to represent Π, what integer-value of x would give us
the closest approximation?
3. How many positive integers are less than 10Π?
3.14159265358979
4. If Tony memorized 85 digits of Π, and he recited them in exactly
18 seconds, then he recited them at the average rate of how many
digits per second? Express your answer to the nearest whole number.
5. A particular circle’s circumference is 4Π inches, and its area is 4Π square inches.
What is the radius of the circle, in inches?
6. Pam Piper prepared a plum pie in a circular pan with a diameter of 9 inches.
If the pie piece that Polly Peters purchased from Pam Piper was Π square inches
on the bottom, what percent of Pam Piper’s prepared plum pie did Polly Peters
purchase? Express your answer to the nearest whole number.
**The following problems are all from Volume I of the 2007-2008 MATHCOUNTS School Handbook. **
7. What is the area, in square units, of the circle that is centered at the origin and
is tangent to the line y = 7? Express your answer in terms of Π.
8. Four congruent quarter-circles are drawn inside a square of side
length 4 cm, as shown. What is the area of the shaded portion of the
square region, in sq cm? Express your answer in terms of Π.
9. This square has an area of 49 square centimeters. What is the area of the
inscribed circle, in sq cm? Express your answer as a decimal to the nearest
tenth.
10. The formula for the total surface area of a cylinder is SA = 2Πr 2 + 2Πrh, where
r is the radius and h is the height. A particular solid right cylinder of radius 2 feet
has a total surface area of 12Π square feet. What is the height of the cylinder, in
feet?
Copyright MATHCOUNTS, Inc. 2007. All rights reserved. MATHCOUNTS Club Resource Guide Problem Set