To find the diameter of the exercise ball given its surface area, we can use the formula for the surface area of a sphere, which is:
\[ A = 4 \pi r^2 \]
where \(A\) is the surface area and \(r\) is the radius. We are given:
\[ A = 13,266.5 , \text{cm}^2 \] \[ \pi \approx 3.14 \]
Plugging in the values we have:
\[ 13,266.5 = 4 \times 3.14 \times r^2 \]
First, calculate \(4 \times 3.14\):
\[ 4 \times 3.14 = 12.56 \]
Now, we can rewrite the equation as:
\[ 13,266.5 = 12.56 r^2 \]
Next, solve for \(r^2\):
\[ r^2 = \frac{13,266.5}{12.56} \]
Calculating the right side:
\[ r^2 \approx 1056.49 \]
Now, take the square root to find \(r\):
\[ r \approx \sqrt{1056.49} \approx 32.5 , \text{cm} \]
Finally, 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.
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