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📅 May 13, 2026 👤 scraface

May 13, 2026

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

📌 #### 2744 - (1372/3)π

📌 An equilateral triangle with a side length of 10 cm has a circle inscribed within it. What is the area of the circle?

📌 Area of equilateral triangle = (√3/4) × (10 cm)^2 = 25√3 square cm

📌 Radius of inscribed circle (inradius) = (side × √3) / 6 = (10√3) / 6 = (5√3) / 3 cm

📌 Area of the circle = π × [(5√3) / 3]^2 = π × (25 × 3) / 9 = (75/9)π = (25/3)π square cm

📌 #### (25/3)π

📌 A pyramid with a square base of side 6 cm and height 9 cm is filled with water. If this water is poured into a cone with a radius of 3 cm, what is the height of the water in the cone?

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