The surface area of an exercise ball is 13,266.5 cm2

. Using 3.14 as the value of pi, what is the diameter of the exercise ball?(1 point)
Responses

65 cm
65 cm

32.5 cm
32.5 cm

36.7 cm
36.7 cm

28.8 cm

1 answer

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 \( \pi \approx 3.14 \):

  1. Calculate \( r^2 \):

\[ r^2 = \frac{13266.5}{4 \times 3.14} = \frac{13266.5}{12.56} \approx 1056.46 \]

  1. Now, find \( r \):

\[ r \approx \sqrt{1056.46} \approx 32.5 \text{ cm} \]

  1. 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.