The diameter of a circle is 8 millimetres. What is the circle's area?d=8 mmUse ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

1. Break Down the Problem

To find the area of a circle, we need to use the formula: $A = \pi r^2$ where $A$ is the area and $r$ is the radius. Since the diameter is given, we'll first need to calculate the radius.

2. Relevant Concepts

1. Radius Calculation: The radius $r$ is half of the diameter $d$. $r = \frac{d}{2}$
2. Area Calculation: Once we have the radius, we will substitute it into the area formula.

3. Analysis and Detail

1. Calculate the Radius: $r = \frac{8 \text{ mm}}{2} = 4 \text{ mm}$

2. Substitute into Area Formula: $A = \pi (4 \text{ mm})^2$ $A = 3.14 \times 16 \text{ mm}^2$ $A = 50.24 \text{ mm}^2$

4. Verify and Summarize

The calculations appear correct. The area of the circle, rounded to the nearest hundredth, is $50.24 \text{ mm}^2$.

Final Answer

The area of the circle is 50.24 mm².