Question

длина линии пересечения сферы и плоскости проходящей через конец диаметра под углом 60° к нему, равна 7π см. найдите диаметр сферы , площадь поверхности сферы, объем шара, ограниченного данной сферой

Answer 1

Відповідь додаю на фото

Answer 2

This is a geometry problem that requires some calculations and drawings. I will try to answer it as detailed as possible, using the information from the web search results.

First, let's draw a sketch of the given situation. We have a sphere with a diameter AB and a plane that passes through point B and forms an angle of 60° with AB. The plane intersects the sphere in a circle with diameter BC. We are given that the length of BC is 7π cm.

![sketch]

To find the diameter of the sphere, we can use the Pythagorean theorem on the right triangle ABC. We have:

AB² = AC² + BC²

AC is the radius of the sphere, so we can write:

(2AC)² = AC² + (7π)²

Simplifying and solving for AC, we get:

AC = √(49π²/3) cm

Therefore, the diameter of the sphere is:

AB = 2AC = 2√(49π²/3) cm ≈ 25.67 cm

To find the surface area of the sphere, we can use the formula:

S = 4πr²

where r is the radius of the sphere. Substituting AC for r, we get:

S = 4π(√(49π²/3))²

S = 196π³/3 cm² ≈ 2045.24 cm²

To find the volume of the ball bounded by the sphere, we can use the formula:

V = (4/3)πr³

where r is the radius of the sphere. Substituting AC for r, we get:

V = (4/3)π(√(49π²/3))³

V = (343/9)√3 π⁴ cm³ ≈ 8495.87 cm³

I hope this answer helps you understand how to solve this problem. If you want to learn more about geometry, you can check out these sources:

- [РЕШЕНИЕ ТИПОВЫХ ЗАДАЧ НАЧЕРТАТЕЛЬНОЙ ГЕОМЕТРИИ](https://rep.bntu.by/bitstream/handle/data/3679/Reshenie_tipovyh_zadach_nachertatelnoj_geometrii.pdf?sequence=7) - [Начертательная геометрия Flashcards](https://quizlet.com/349015907/%D0%9D%D0%B0%D1%87%D0%B5%D1%80%D1%82%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F-%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F-flash-cards/)

: This is a sketch I made using `graphic_art` tool.