Question

The surface area of an exercise ball is 13,266.5 cm^2. Using 3.14 as the value of pi, what is the diameter of the exercise ball?

Answer 1

To find the diameter of the exercise ball based on 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.

We're given that the surface area \( A = 13,266.5 \, \text{cm}^2 \). We need to solve for the radius \( r \) first and then find the diameter \( d \) using the relationship \( d = 2r \).

1. Substitute the known values into the surface area formula:

\[
13,266.5 = 4 \times 3.14 \times r^2
\]

2. Calculate \( 4 \times 3.14 \):

\[
4 \times 3.14 = 12.56
\]

Thus, the equation simplifies to:

\[
13,266.5 = 12.56 \times r^2
\]

3. Now, solve for \( r^2 \):

\[
r^2 = \frac{13,266.5}{12.56}
\]

Calculating the right-hand side:

\[
r^2 \approx \frac{13,266.5}{12.56} \approx 1,056.0
\]

4. Take the square root to find \( r \):

\[
r \approx \sqrt{1,056.0} \approx 32.5 \, \text{cm}
\]

5. Finally, calculate the diameter \( d \):

\[
d = 2r = 2 \times 32.5 = 65.0 \, \text{cm}
\]

Hence, the diameter of the exercise ball is approximately **65.0 cm**.