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Let's break this down:

### Given:
- Radius of the **larger circle** = 16 meters
- Diameter of the **smaller circle** = 28 meters

From this information:
- **Radius of the smaller circle** = 28 ÷ 2 = 14 meters

### Part (a): How long is the bigger circle compared to the smaller circle?

To find the length (circumference) of each circle, we use the formula for circumference:  
\[
C = 2 \pi r
\]

- Circumference of the **larger circle**:
\[
C_{\text{larger}} = 2 \pi \times 16 = 32\pi \text{ meters}
\]

- Circumference of the **smaller circle**:
\[
C_{\text{smaller}} = 2 \pi \times 14 = 28\pi \text{ meters}
\]

Now, to compare the circumferences:
\[
\frac{C_{\text{larger}}}{C_{\text{smaller}}} = \frac{32\pi}{28\pi} = \frac{32}{28} = \frac{8}{7}
\]

Thus, the larger circle is \(\frac{8}{7}\) times longer than the smaller circle.

### Part (b): Difference in area between the larger and smaller circle

To find the area of each circle, we use the formula for the area of a circle:  
\[
A = \pi r^2
\]

- Area of the **larger circle**:
\[
A_{\text{larger}} = \pi \times 16^2 = \pi \times 256 = 256\pi \text{ square meters}
\]

- Area of the **smaller circle**:
\[
A_{\text{smaller}} = \pi \times 14^2 = \pi \times 196 = 196\pi \text{ square meters}
\]

The difference in the area is:
\[
A_{\text{difference}} = 256\pi - 196\pi = 60\pi \text{ square meters}
\]

So, the difference in area between the larger and smaller circle is \(60\pi\) square meters, approximately:
\[
60\pi \approx 188.4 \text{ square meters}
\]

### Summary:
1. The larger circle is \(\frac{8}{7}\) times longer than the smaller circle.
2. The difference in area between the larger and smaller circle is approximately 188.4 square meters.

Would you like more details or have any questions?

Here are some related questions you might find useful:
1. What is the total area of both circles combined?
2. How would the result change if the diameter of the smaller circle increased by 10%?
3. How does the ratio of circumferences relate to the ratio of areas?
4. What is the area of the circular driveway (the area between the two circles)?
5. How would the circumference comparison change if the radius of the larger circle doubled?

**Tip:** Always use the exact value of \(\pi\) for precise results in problems involving circles. Approximate \(\pi\) when an estimation is required.

A circular driveway is bounded by two circles. The illustration indicates that the radius of the larger circle is 16 meters, and the diameter of the smaller circle is 28 meters.

If you tried to drive, how long is the bigger circle compared to the smaller circle?
What is the difference of the area between the larger and smaller circle?

Solve a problem involving two circles: the larger circle has a radius of 16 meters and the smaller circle has a diameter of 28 meters. Learn how to compare their circumferences and calculate the difference in areas using formulas for circles. Suitable for students in Grades 8-10.

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