Предмет: Геометрия, автор: tylik

Три шара с радиусами 3 см, 5 см, 12 см попарно касаются друг друга. Найдите поверхность шара, проходящего через все центры данных шаров.

Ответы

Автор ответа: mike2

См. рисунок:

ОО1=а=15+5=20

О1О2=b=5+3=8

O2O=3+15=18

p=a+b+c=20+18+8=46

Находим в треуг. ОО1О2 радиус описанной окружности R:

R=abc/sqrt(p(p-2a)(p-2b)(p-2c))=48/sqrt(23)

Теперь площадь сферы с этим радиусом:

S=4ПR^2=9216П/23

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