https://file.aiquickdraw.com/mathbot/file/1726381936429v0z1c1ad.jpg

Let’s solve each of the questions based on the image:

### 1. For **radius = 5 cm**:
The formula for the **circumference** of a circle is:
\[
C = 2\pi r
\]
Where \(r\) is the radius and \(\pi \approx 3.1416\).

\[
C = 2 \times 3.1416 \times 5 = 31.42 \, \text{cm}
\]
**Circumference = 31.42 cm**

---

### 2. For **radius = 2 m**:
The formula for the **area** of a circle is:
\[
A = \pi r^2
\]
\[
A = 3.1416 \times (2)^2 = 3.1416 \times 4 = 12.57 \, \text{m}^2
\]
**Area = 12.57 m²**

---

### 3. For **diameter = 20 km**:
The diameter \(d\) is related to the radius by \(d = 2r\), so the radius \(r = \frac{d}{2} = 10 \, \text{km}\).

Using the formula for the circumference:
\[
C = 2\pi r = 2 \times 3.1416 \times 10 = 62.83 \, \text{km}
\]
**Circumference = 62.83 km**

---

### 4. For **diameter = 1 mm**:
Again, using \(d = 2r\), the radius \(r = \frac{1}{2} = 0.5 \, \text{mm}\).

Now, calculate the area:
\[
A = \pi r^2 = 3.1416 \times (0.5)^2 = 3.1416 \times 0.25 = 0.7854 \, \text{mm}^2
\]
**Area = 0.79 mm²** (rounded to two decimal places)

---

Would you like more details or have any further questions? Here are five related questions for further exploration:

1. How does changing the radius affect the circumference and area of a circle?
2. What would the area be if the radius was doubled in question 2?
3. What is the circumference of a circle with a diameter of 15 cm?
4. How would you calculate the area if the diameter, instead of the radius, is given?
5. Can you express the area of a circle in terms of its circumference?

**Tip:** Always remember that the circumference is directly proportional to the radius, while the area depends on the square of the radius.

Given problems based on calculating the circumference and area of circles with different radii and diameters.

Learn how to calculate the circumference and area of circles with given radii and diameters. Explore detailed solutions using key geometry concepts such as the formulas C = 2πr for circumference and A = πr² for area. Perfect for students in Grades 6-8.

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