Боковое ребро правильной треугольной призмы - 2 м, сторона основания - 3м. Найти диаметр описанного шара. Помогите пожалуйста!!!!

Боковое ребро правильной треугольной призмы - 2 м, сторона основания - 3м. Найти диаметр описанного шара.
Помогите пожалуйста!!!!
- Предмет:
  Геометрия
- Автор:
  jessica
- 5 лет назад

Ответы 1

Основания призмы АВС и А₁В₁С₁ - правильные треугольники, касаются вершинами поверхности сферы. О₂А и О₁А₁ - радиусы описанных окружностей около оснований. R=a√3/3.О₂А=АВ√3/3=3√3/3=√3 м.О₁О₂=h=2 ⇒ OO₂=h/2=1 м.ОА - радиус шара.В прямоугольном тр-ке AOO₂ AO²=AO₂²+OO₂²=3+1=4,АО=2 м - это ответ.
- Автор:
  oswaldozimmerman
- 5 лет назад
- 0
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Боковое ребро правильной треугольной призмы - 2 м, сторона основания - 3м. Найти диаметр описанного шара. Помогите пожалуйста!!!!

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Боковое ребро правильной треугольной призмы - 2 м, сторона основания - 3м. Найти диаметр описанного шара.
Помогите пожалуйста!!!!