Question

Радиус шара 13 см. Найти площадь сечения шара плоскостью, удалённой от центра шара на 12 см.

Answer 1

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Answer 2

Calculation of the Cross-Sectional Area of a Sphere

To find the cross-sectional area of a sphere with a radius of 13 cm, where the plane is located 12 cm away from the center of the sphere, we can use the formula for the area of a circle.

The cross-sectional area of a sphere is equal to the area of a circle with a radius equal to the distance from the center of the sphere to the plane.

The formula for the area of a circle is:

A = πr^2

Where: - A is the area of the circle - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the circle

In this case, the radius of the circle is 12 cm, which is the distance from the center of the sphere to the plane.

Let's calculate the cross-sectional area of the sphere using this formula:

A = π(12^2)

Calculating this expression gives us:

A ≈ 452.38934 cm^2

Therefore, the cross-sectional area of the sphere, with a plane located 12 cm away from the center, is approximately 452.38934 square centimeters.

Please note that the result is an approximation and rounded to five decimal places.

Conclusion

The cross-sectional area of a sphere, with a radius of 13 cm, when a plane is located 12 cm away from the center of the sphere, is approximately 452.38934 square centimeters.