Question

ЯСНО И ПОНЯТНО! В шаре радиуса 25 дм проведена секущая плоскость, которая делит перпендикулярный ей диаметр в отношении 2:3. Найдите площадь сечения шара этой плоскостью. Желательно на листочке и фото скинуть сюда. СО ВСЕМИ ФОРМУЛАМИ И ПОДРОБНЫМ РЕШЕНИЕМ!

Answer 1

АВ - диаметр
АВ=2·R=2·25 дм= 50 дм

АК:КВ=2:3 по условию
АК=(2/5)·AB=(2/5)·50=20 дм


КО=АО-АК=25-20=5 дм

По теореме Пифагора
МК²=МО²-ОК²=25²-5²=625-25=600
МК=√600=10√6 дм

r=MK

S(сечения)=πr²=π·(10√6)²=600π кв дм

Answer 2

Finding the Area of the Cross-Section of a Sphere

To find the area of the cross-section of a sphere, we need to consider the properties of the sphere and the given information about the intersecting plane.

Let's break down the problem step by step:

1. We have a sphere with a radius of 25 dm (decimeters). 2. A cutting plane has been drawn through the sphere, dividing a perpendicular diameter in a ratio of 2:3.

To find the area of the cross-section, we need to determine the radius of the circle formed by the intersection of the cutting plane with the sphere. Once we have the radius, we can calculate the area of the circle using the formula for the area of a circle.

Calculating the Radius of the Cross-Section Circle

To calculate the radius of the cross-section circle, we can use the given ratio of 2:3 to find the lengths of the two segments of the diameter.

Let's assume the length of the perpendicular diameter is D. According to the given ratio, one segment of the diameter is 2/5 of D, and the other segment is 3/5 of D.

Therefore, the lengths of the two segments are:

Segment 1: (2/5) * D Segment 2: (3/5) * D

Since the sum of the lengths of the two segments is equal to the diameter D, we can write the equation:

(2/5) * D + (3/5) * D = D

Simplifying the equation, we get:

(2/5 + 3/5) * D = D

(5/5) * D = D

D = D

This equation tells us that the lengths of the two segments are equal, which means the cutting plane passes through the center of the sphere. Therefore, the cross-section is a circle with a radius equal to the radius of the sphere.

Calculating the Area of the Cross-Section Circle

Since the radius of the cross-section circle is equal to the radius of the sphere (25 dm), we can calculate the area of the cross-section circle using the formula for the area of a circle:

Area = π * r^2

where π is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

Substituting the value of the radius (25 dm) into the formula, we get:

Area = 3.14159 * (25 dm)^2

Calculating the area, we find:

Area ≈ 3.14159 * 625 dm^2

Area ≈ 1963.495 dm^2

Therefore, the area of the cross-section of the sphere formed by the cutting plane is approximately 1963.495 square decimeters.

Please note that the calculations provided above are based on the given information and assumptions made. If there are any additional details or constraints, please let me know, and I'll be happy to assist you further.