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Home » Thus, the smallest such \( N \) is: - Veritas Home Health

Thus, the smallest such \( N \) is: - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Volume = \( \frac{1}{3} \times 36 \times 10 = 120 \) cubic meters.

📌 The base area of the rectangular container is \( 3 \times 4 = 12 \) square meters.

📌 The height of the sand layer is \( \frac{120}{12} = 10 \) meters.

📌 A cone with a radius of 4 cm and a height of 9 cm is melted to form a sphere. What is the radius of the sphere?

📌 Volume of the cone is \( V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \times 4^2 \times 9 = 48\pi \) cubic centimeters.

📌 Volume of the sphere is \( V = \frac{4}{3} \pi R^3 \).

📌 Setting the volumes equal: \( \frac{4}{3} \pi R^3 = 48\pi \).

📌 Solving for \( R^3 \), we get \( R^3 = 36 \), so \( R = \sqrt[3]{36} \approx 3.301 \) cm.

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