Каково отношение объемов двух шаров, если их диаметры имеют соотношение 2:5?

Содержание: Отношение объемов шаров

Описание: Для того чтобы найти отношение объемов двух шаров, необходимо знать, что объем шара можно вычислить по формуле V = (4/3)πr³, где V - объем шара, π - число пи (приближенное значение 3.14), r - радиус шара. Также необходимо знать, что диаметр шара равен удвоенному радиусу, то есть d = 2r.

Пусть у первого шара диаметр равен 2a, а у второго шара - 5a. Тогда радиус первого шара будет равен a, а радиус второго шара - 5a/2.
Подставляя значения радиусов в формулу для объема шара, получаем следующие выражения:
V₁ = (4/3)πa³
V₂ = (4/3)π(5a/2)³

Сокращая выражения и выполняя необходимые вычисления, получаем:
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