#### 2744 - (1372/3)π

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• 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
• 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

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