To find the cross-sectional area of a sphere that passes through its center, we need to use the formula for the area of a circle, since the cross-section at the center is a circle.
The formula for the area A of a circle is:
A = πr²
Where:
- A is the area of the circle.
- r is the radius of the circle.
- π (pi) is a constant approximately equal to 3.14159.
In this case, the radius of the sphere is given as 6.17 meters. Therefore, we can substitute this value into the formula:
A = π(6.17)²
A = π(38.0489)
A ≈ 3.14159 × 38.0489
A ≈ 119.049 square meters.
So, the cross-sectional area that passes through the center of the sphere is approximately 119.05 square meters.