Осевое сечение конуса представляет собой равнобедренный треугольник, боковые стороны которого равны образующей конуса, основание равно диаметру основания конуса.
Площадь осевого сечения равна половине произведения высоты конуса на диаметр его основания:
S = 0,5 * h * d = 0,5 * h * 2 * r = h * r.
Зная значения площади осевого сечения и радиуса основания, найдем высоту:
h = S / r = 8 / 2 = 4.
Образующая конуса l, радиус основания r и высота h образуют прямоугольный треугольник, для которого по теореме Пифагора:
l2 = h2 + r2 = 42 + 22 = 16 + 4 = 20;
l = √20 = 2√5.
Площадь боковой поверхности конуса равна произведению образующей на половину длины окружности основания:
S = п * r * l = п * 2 * 2√5 = 4п√5 ≈ 28,1.
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11 класс английский язык
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