The circumference of a circle can be calculated using the formula:
\[ C = \pi d \]
where \(C\) is the circumference and \(d\) is the diameter.
From the problem, we know that when the diameter is 5, the circumference is approximately 15.7. Using this information, we can estimate the value of \(\pi\):
\[ 15.7 = \pi \times 5 \]
To find \(\pi\):
\[ \pi \approx \frac{15.7}{5} \approx 3.14 \]
Now, we can use this approximation of \(\pi\) to find the circumference of a circle with a diameter of 9:
\[ C = \pi \times d \approx 3.14 \times 9 \]
Calculating this gives:
\[ C \approx 3.14 \times 9 \approx 28.26 \]
Rounding this to the nearest tenth:
\[ C \approx 28.3 \]
Thus, the approximate circumference of a circle with a diameter of 9 is:
\[ \boxed{28.3} \]