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Консультация № 195810
05.06.2019, 11:54
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Угол между высотой правильной треугольной пирамиды и апофемой равен альфа, длина бокового ребра пирамиды равна L. Найти объем пирамиды.
Угол между высотой правильной треугольной пирамиды и апофемой равен альфа, длина бокового ребра пирамиды равна L. Найти объем пирамиды.
Обсуждение
08.06.2019, 10:16
общий
это ответ
Здравствуйте, salomatkina1998!
Длина проекции апофемы на плоскость основания пирамиды составляет r=L*sin[$945$], а длина высоты пирамиды -- H=L*cos[$945$]. Согласно [1, с. 13], r=a[$8730$]3/6; поэтому a=6r/[$8730$]3=6L*sin[$945$]/[$8730$]3 -- длина стороны равностороннего треугольника, являющегося основанием пирамиды; S=a2[$8730$]3/4=[$8730$]3/4*(6L*sin[$945$]/[$8730$]3)2=3[$8730$]3L2sin2[$945$] -- площадь основания пирамиды; согласно [1, с. 16], объём пирамиды составляет
Поясняющий рисунок находится в прикреплённом файле.
Литература
1. Цыпкин А. Г., Цыпкин Г. Г. Математические формулы. -- М.: Наука, 1985. -- 128 с.
Длина проекции апофемы на плоскость основания пирамиды составляет r=L*sin[$945$], а длина высоты пирамиды -- H=L*cos[$945$]. Согласно [1, с. 13], r=a[$8730$]3/6; поэтому a=6r/[$8730$]3=6L*sin[$945$]/[$8730$]3 -- длина стороны равностороннего треугольника, являющегося основанием пирамиды; S=a2[$8730$]3/4=[$8730$]3/4*(6L*sin[$945$]/[$8730$]3)2=3[$8730$]3L2sin2[$945$] -- площадь основания пирамиды; согласно [1, с. 16], объём пирамиды составляет
V=1/3*SH=1/3*3[$8730$]3L2sin2[$945$]*L*cos[$945$]=[$8730$]3L3sin2[$945$]cos[$945$] (ед. объёма).
Поясняющий рисунок находится в прикреплённом файле.
Литература
1. Цыпкин А. Г., Цыпкин Г. Г. Математические формулы. -- М.: Наука, 1985. -- 128 с.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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