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Home » $5 \cdot 7 \cdot 9 \cdot 11 = 3465$ - Red Crowns

$5 \cdot 7 \cdot 9 \cdot 11 = 3465$ - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Un ballon sphérique est gonflé de sorte que son volume augmente à un rythme de 10 cm³/s. À quelle vitesse le rayon du ballon augmente-t-il lorsque le rayon est de 5 cm ?

📌 Le volume V d'une sphère est donné par V = 4/3πr³.

📌 En dérivant par rapport au temps, dV/dt = 4πr²(dr/dt).

📌 Étant donné dV/dt = 10 cm³/s, et r = 5 cm, substituer dans l'équation dérivée.

📌 = 4π(5)²(dr/dt) = 100π(dr/dt).

📌 En résolvant pour dr/dt, dr/dt = 10 / (100π) = 0,01 / π ≈ 0,00318 cm/s.

📌 Le rayon augmente à un rythme de 0,00318 cm/s lorsque le rayon est de 5 cm.

📌 #### 0,00318 cm/s

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