To find the diameter of the exercise ball given its surface area, we can use the formula for the surface area of a sphere:
\[ A = 4 \pi r^2 \]
where \( A \) is the surface area and \( r \) is the radius. We can rearrange this formula to solve for the radius:
\[ r^2 = \frac{A}{4\pi} \]
Then, to find the diameter \( d \), we can use:
\[ d = 2r \]
Given that the surface area \( A \) is 13,266.5 cm² and using \( \pi \approx 3.14 \):
- Calculate \( r^2 \):
\[ r^2 = \frac{13266.5}{4 \times 3.14} = \frac{13266.5}{12.56} \approx 1056.46 \]
- Now, find \( r \):
\[ r \approx \sqrt{1056.46} \approx 32.5 \text{ cm} \]
- Finally, calculate the diameter \( d \):
\[ d = 2r \approx 2 \times 32.5 \approx 65 \text{ cm} \]
Therefore, the diameter of the exercise ball is 65 cm.