What is the circumference of a one-dollar coin to the nearest hundredth of a millimeter if the diameter is 26.5 millimeters?

Understand the Problem

The question is asking us to calculate the circumference of a one-dollar coin given its diameter of 26.5 millimeters. We will use the formula for the circumference of a circle, which is C = π * d, where C is the circumference and d is the diameter. Once calculated, we will round the answer to the nearest hundredth of a millimeter.

Answer

$83.41 \text{ mm}$

Steps to Solve

Identify the formula for circumference

We will use the formula for the circumference of a circle, which is given by:

$$ C = \pi \times d $$

where $C$ is the circumference and $d$ is the diameter.

Substitute the diameter value into the formula

Given the diameter of the coin is 26.5 millimeters, we substitute this value into the formula:

$$ C = \pi \times 26.5 $$

Calculate π times the diameter

Using the approximate value of π, which is about 3.14, we can calculate:

$$ C \approx 3.14 \times 26.5 $$

Perform the multiplication

Calculating the above expression:

$$ C \approx 3.14 \times 26.5 \approx 83.41 $$

Round the answer to the nearest hundredth

Since the result is already at two decimal places, the final circumference rounded to the nearest hundredth of a millimeter is:

$$ C \approx 83.41 \text{ mm} $$

The circumference of the one-dollar coin is approximately $83.41 \text{ mm}$.

More Information

The formula for the circumference of a circle is fundamental in geometry and is essential for understanding properties of circular shapes. The circumference of a coin is important for various applications such as minting and design specifications.

Tips

Using the wrong value for π: Make sure to use an accurate value, like 3.14 or 3.14159.
Forgetting to round properly: Always check if the problem specifies a certain number of decimal places for rounding.

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