When Meg won a contest, she got a silver medal with a radius of 7.2 centimeters. What is the medal's area?

1. Break Down the Problem

To find the area of the medal, we need to apply the formula for the area of a circle, which is given by:

$A = \pi r^2$

where $A$ is the area and $r$ is the radius.

2. Relevant Concepts

The formula for the area of a circle involves the mathematical constant $\pi$ (approximately 3.14159) and the radius of the circle.

3. Analysis and Detail

We know that the radius $r$ of the medal is 7.2 cm. Now, we can substitute this value into the area formula:

$A = \pi (7.2 \, \text{cm})^2$

Calculating $(7.2)^2$:

$(7.2)^2 = 51.84 \, \text{cm}^2$

Now, substituting this back into the area formula:

$A = \pi \times 51.84 \, \text{cm}^2$

Using $\pi \approx 3.14159$:

$A \approx 3.14159 \times 51.84 \approx 162.65 \, \text{cm}^2$

4. Verify and Summarize

The calculations have been carried out correctly, yielding an area of the medal about 162.65 square centimeters.

Final Answer

The area of the medal is approximately $162.65 \, \text{cm}^2$.