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,
- \( r \) is the radius,
- \( \pi \) is approximately 3.14.
Given that the surface area \( A = 13,266.5 , \text{cm}^2 \), we can rearrange the formula to solve for the radius \( r \):
\[ r^2 = \frac{A}{4\pi} \]
Substituting the values we have:
\[ r^2 = \frac{13,266.5}{4 \times 3.14} \]
Calculating the denominator:
\[ 4 \times 3.14 = 12.56 \]
Now substituting that back into the equation for \( r^2 \):
\[ r^2 = \frac{13,266.5}{12.56} \approx 1056.65 \]
Now taking the square root to find \( r \):
\[ r \approx \sqrt{1056.65} \approx 32.5 , \text{cm} \]
The diameter \( d \) is twice the radius:
\[ d = 2r \approx 2 \times 32.5 \approx 65 , \text{cm} \]
Thus, the diameter of the exercise ball is:
65 cm