Question

Шар диаметром 20см пересечен плоскостью отстоящей от его центра на 6 см найти площадь полученного сечения

Answer 1

1) треугольник АОВ-прямоугольный, угол А=90(градусов)
по теореме Пифагора: AB=$\sqrt{ 10^{2} - 6^{2} }= \sqrt{64} =8$
2) S(сечения)=$\pi R^{2}$=$\pi * 8^{2}$=$64\pi$

Answer 2

Finding the Area of the Cross-Section

To find the area of the cross-section of a sphere with a diameter of 20 cm intersected by a plane 6 cm away from its center, we can use the following approach:

1. Identify the Relevant Formula: - The area of the cross-section of a sphere can be calculated using the formula: \[ A = \pi r^2 - \pi h^2 \] where \( r \) is the radius of the sphere and \( h \) is the distance from the center of the sphere to the plane.

2. Calculate the Radius of the Sphere: - Since the diameter of the sphere is given as 20 cm, the radius \( r \) can be calculated as half of the diameter: \[ r = \frac{20}{2} = 10 \, \text{cm} \]

3. Calculate the Area of the Cross-Section: - Using the formula, we can substitute the values of \( r \) and \( h \) to find the area of the cross-section.

Calculation

The area of the cross-section can be calculated as follows: \[ A = \pi \times 10^2 - \pi \times 6^2 \]

\[ A = 100\pi - 36\pi \]

\[ A = 64\pi \]

Result

Therefore, the area of the cross-section of the sphere is 64π square centimeters.