Problem Solving Circles
Official US Coins
Below are some examples of US money, both
coins and paper money.
The following Math Lab uses US coins to solve
problems with circles.
US money has been around
since the mid 1600’s when
our country was first
established. We used
English, Spanish, and
French monies. The
Massachusetts Bay Colony
first issued paper money
which would later help form
the United States.
US coins have been around since the 1650’s.
These coins below were first minted in New
England in 1652.
Official US Coin Sizes
Coin
Diameter (mm)
Penny
19
Nickel
21
Dime
28
Quarter
24
Half Dollar
31
Dollar
27
Use the table to
answer each question.
Use 3.14 for π
1) Which coin has the
smallest radius? How long
is that coin’s radius?
2) What is the
circumference of a
nickel?
3) What is the area of a
quarter?
4) Which coin has a
greater area, a dollar or
half dollar? What is the
difference in their areas?
Official US Coin Sizes
Coin
Diameter (mm)
Penny
19
Nickel
21
Dime
28
Quarter
24
Half Dollar
31
Dollar
27
Use the table to
answer each question.
Use 3.14 for π
5) If you rolled a dollar
coin on its edge, how far
would it go each complete
revolution (roll)?
6) Which US coins will fit
in a vending machine slot
that is 2 centimeters wide?
7) An engraving of Thomas
Jefferson’s home,
Monticello, covers about
1/3 of a nickel’s tails side.
What is the area of the
Monticello etching?
Official US Coin Sizes
Coin
Diameter (mm)
Penny
19
Nickel
21
Dime
28
Quarter
24
Half Dollar
31
Dollar
27
Use the table to
answer each question.
Use 3.14 for π
8) The engraved words
“United States of America”
run about one-half the
circumference of all US
coins. On which coin will the
words run about 38 mm?
9) A dime has 118 ridges
evenly spaced along its
circumference. About how
wide is each ridge?
a. 0.24 mm
b. 0.48mm c. 0.15mm d. 0.08mm
10) Your two coins together
cover an area of about
540mm2. How much money do
you have?
a. $0.11 b. $1.10 c. $1.50 d. $0.35