Вопрос школьника по предмету Математика
Радиус окружности равен 5 см на сколько процентов уменьшится площадь круга, ограниченного этой окружностью ,если её радиус уменьшиться на 1 процент.
Ответ учителя по предмету Математика
Исходный радиус R = 5cм, площадь круга S =πR² = 25π (см²)
Уменьшение исходного радиуса ΔR = 0.01R = 0.05см
Новый радиус R1 = R — ΔR = 5 — 0.05 = 4.95 (см)
Новая площадь круга S1 = π·R1² = 24.5025 (cм²)
Разница площадей ΔS = S — S1 = 25π — 24.5025π = 0.4975π (см²)
Теперь найдём, на сколько процентов уменьшится площадь:
(ΔS/S)·100% = (0.4975π/25π) · 100% = 1.99%
Ответ: Площадь уменьшится на 1,99%
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