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Home » \( \theta = 30^\circ \) (angle) - RoadRUNNER Motorcycle Touring & Travel Magazine

\( \theta = 30^\circ \) (angle) - RoadRUNNER Motorcycle Touring & Travel Magazine

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 Height of smaller cone = 9 cm / 2 = 4.5 cm

📌 Radius of smaller cone (proportional) = 4 cm / 9 cm × 4.5 cm = 2 cm

📌 Volume of smaller cone = (1/3)π × (2 cm)^2 × 4.5 cm = 6π cubic cm

📌 A sphere with a radius of 7 cm is inscribed in a cube. What is the volume of the cube not occupied by the sphere?

📌 Side length of the cube = 2 × radius of sphere = 14 cm

📌 Volume of the cube = 14 cm × 14 cm × 14 cm = 2744 cubic cm

📌 Volume of the sphere = (4/3)π × (7 cm)^3 = (4/3)π × 343 = (1372/3)π cubic cm

📌 Unoccupied volume = Volume of cube - Volume of sphere = 2744 - (1372/3)π cubic cm

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