The United States Treasury Department set the dimensions of a one-dollar coin in 1979. A one-dollar coin has a diameter that measures 26.5 millimeters. What is the circumference of... The United States Treasury Department set the dimensions of a one-dollar coin in 1979. A one-dollar coin has a diameter that measures 26.5 millimeters. What is the circumference of the coin to the nearest hundredth of a millimeter?
Understand the Problem
The question is asking to calculate the circumference of a one-dollar coin based on its diameter using the formula for the circumference of a circle, which is C = πd. Here, the diameter is given as 26.5 millimeters, and the answer needs to be rounded to the nearest hundredth of a millimeter.
Answer
The circumference of the coin is $83.11$ mm.
Answer for screen readers
The circumference of the one-dollar coin is approximately $83.11$ millimeters.
Steps to Solve
-
Identify the Circumference Formula
The circumference ($C$) of a circle can be calculated using the formula:
$$ C = \pi d $$
where $d$ is the diameter of the circle. -
Plug in the Diameter
The diameter of the one-dollar coin is given as 26.5 millimeters. Substitute this value into the formula:
$$ C = \pi \times 26.5 $$ -
Calculate the Circumference
Using the value of $\pi \approx 3.14159$, perform the multiplication:
$$ C \approx 3.14159 \times 26.5 \approx 83.113235 $$ -
Round to Nearest Hundredth
To round 83.113235 to the nearest hundredth, look at the third decimal place:
Since it's a 3 (which is less than 5), we round down:
$$ C \approx 83.11 $$
The circumference of the one-dollar coin is approximately $83.11$ millimeters.
More Information
The formula for the circumference of a circle is widely used in various practical applications, from calculating the distance traveled around circular paths to determining the material needed for circular objects. The one-dollar coin's design and dimensions are standardized, making it a common example in geometry.
Tips
- Confusing diameter with radius: Always ensure to use the correct measurement in the formula.
- Not rounding correctly: Remember to look at the third decimal place to decide how to round the second decimal place.
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