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Home » 但顶角 $60^\circ$ 实际表示圆锥的几何特征： - Aurero

但顶角 $60^\circ$ 实际表示圆锥的几何特征： - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Equating volumes: 108 = 3πh

📌 Solving for h: h = 108 / (3π) = 36 / π cm

📌 A rectangular prism has dimensions 8 cm by 6 cm by 4 cm. If a cylindrical hole with a radius of 1 cm is drilled through the center along the longest dimension, what is the remaining volume?

📌 Volume of prism = 8 cm × 6 cm × 4 cm = 192 cubic cm

📌 Volume of cylindrical hole = π × (1 cm)^2 × 8 cm = 8π cubic cm

📌 Remaining volume = 192 cubic cm - 8π cubic cm

📌 #### 192 - 8π

📌 Volume of frustum = (1/3)πh(R^2 + r^2 + Rr) = (1/3)π × 7 × (5^2 + 3^2 + 5 × 3) = (1/3)π × 7 × (25 + 9 + 15) = (1/3)π × 7 × 49 = 343π/3 cubic cm

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