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.
Given that the surface area \(A = 13,266.5 , \text{cm}^2\) and using \(\pi \approx 3.14\), we can substitute into the formula:
\[ 13,266.5 = 4 \times 3.14 \times r^2 \]
Now, we can simplify and solve for \(r^2\):
\[ 13,266.5 = 12.56 \times r^2 \]
Next, divide both sides by 12.56:
\[ r^2 = \frac{13,266.5}{12.56} \approx 1056.102 \]
Now, take the square root to find \(r\):
\[ r \approx \sqrt{1056.102} \approx 32.5 , \text{cm} \]
Since the diameter \(d\) is twice the radius:
\[ d = 2r \approx 2 \times 32.5 \approx 65 , \text{cm} \]
Therefore, the diameter of the exercise ball is 65 cm.
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