Предмет: Геометрия, автор: 777marat777

диагональ осевого сечения цилиндра равна 12см. Угол между этой диагональю и плоскостью основания равен 30 градусов. Найдите площадь основания цилиндра.

Ответы

Автор ответа: drama46

Высота цилиндра равна длине его образующей. В нашем случае образующая равна 12:2 = 6 см. Угол между образующей и основанием цилиндра прямой, содержит 90 градусов.
Следовательно, диаметр основания равен 12*cos30 = 6 корней из 3. Тогда радиус основания цилиндра равен его половине: 3 корня из 3. И наконец, площадь основания равна 27pi.

Ответ: 27 pi

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