Question

Шар радиуса 17 см пересечен плоскостью, находящейся на расстоянии 8 см от центра. Найдите площадь сечения

Answer 1

R=17см;
d=8
S-?
S=пR^2
r^2=17^2-8^2
r=15см
S=п*15^2=225*п
ответ: 225п

Answer 2

Calculation of the Section Area of a Sphere

To find the area of the section created by a plane intersecting a sphere, we need to consider the radius of the sphere and the distance of the plane from the center of the sphere.

Given: - Radius of the sphere (r) = 17 cm - Distance of the plane from the center of the sphere (d) = 8 cm

To calculate the area of the section, we can use the formula for the area of a circle:

Area of a Circle = π * (radius)^2

However, since the section is not a complete circle, we need to find the fraction of the circle that is included in the section. This fraction can be calculated by dividing the distance of the plane from the center of the sphere by the radius of the sphere.

Fraction of Circle Included in the Section = (distance of plane from center) / (radius)

Let's calculate the fraction of the circle included in the section:

Fraction of Circle Included in the Section = 8 cm / 17 cm

Now, we can calculate the area of the section by multiplying the fraction of the circle included in the section by the area of the complete circle:

Area of the Section = (Fraction of Circle Included in the Section) * (Area of a Circle)

Let's calculate the area of the section:

Area of the Section = (8 cm / 17 cm) * (π * (17 cm)^2)

Using the value of π as approximately 3.14159, we can calculate the area of the section:

Area of the Section ≈ (8 / 17) * (3.14159 * (17)^2) cm^2

Calculating this expression will give us the final answer for the area of the section.

Please note that the above calculation assumes that the section is a circular shape. If the section is a different shape, such as an ellipse, the calculation will be different.

Let me calculate the area of the section for you.