https://file.aiquickdraw.com/mathbot/file/1726163513175vdpefcjv.jpg

The problem is written in Ukrainian and translates as follows:

**Task 38:** A circle has a diameter of 12 cm. Find:
1) The area of the circle;
2) The circumference of the circle.

### Given:
- Diameter \( d = 12 \, \text{cm} \)

### To find:
1. **Area of the circle \( A \)**.
2. **Circumference of the circle \( C \)**.

### Solution:

#### 1. Area of the circle:
The formula for the area of a circle is:

\[
A = \pi r^2
\]

Where \( r \) is the radius of the circle. Since the diameter \( d = 12 \, \text{cm} \), the radius is:

\[
r = \frac{d}{2} = \frac{12}{2} = 6 \, \text{cm}
\]

Now, calculate the area:

\[
A = \pi \times 6^2 = \pi \times 36 \approx 113.1 \, \text{cm}^2
\]

#### 2. Circumference of the circle:
The formula for the circumference is:

\[
C = \pi d
\]

Substitute \( d = 12 \, \text{cm} \):

\[
C = \pi \times 12 \approx 37.7 \, \text{cm}
\]

### Final Answers:
1. The area of the circle is approximately \( 113.1 \, \text{cm}^2 \).
2. The circumference is approximately \( 37.7 \, \text{cm} \).

Let me know if you need further details or have any questions!

Here are five related questions to explore:
1. What is the relationship between radius and diameter of a circle?
2. How would the area change if the diameter was doubled?
3. What is the difference between the area and circumference of a circle?
4. Can you find the radius given the circumference instead of the diameter?
5. How would you compute the area and circumference if you knew only the radius?

**Tip:** Always remember that the diameter is twice the radius, and many circle formulas depend on this relationship!

Круг має діаметр 12 см. Знайдіть: 1) площу круга; 2) довжину кола, що його обмежує.

This problem demonstrates how to find the area and circumference of a circle with a diameter of 12 cm using fundamental circle geometry formulas. The solution covers key concepts such as calculating the area (πr^2) and the circumference (πd), and is suitable for students in Grade 7.

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