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Home » Total lattice points: $2 + 2 = \boxed4$. - Anadea

Total lattice points: $2 + 2 = \boxed4$. - Anadea

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 The ratio of the new volume to the original volume is:

📌 A cone has a base radius of 5 cm and a height of 12 cm. If the cone is sliced parallel to its base at half its height, what is the volume of the smaller cone formed?

📌 A right circular cone is inscribed in a sphere with a radius of 10 cm. If the height of the cone is equal to the diameter of the sphere, find the volume of the cone.

📌 Since the cone is inscribed, the base radius is the distance from the center of the sphere to the base edge, which is:

📌 Re-evaluating, the height from the spheres center to the base is 10 cm, so:

📌 Correcting the setup, the cones height is 20 cm, with its vertex at the spheres center and base at the spheres surface:

📌 A rectangular garden has a length of 24 meters and a width of 15 meters. A walking path 2 meters wide runs along the inside perimeter of the garden. What is the area of the garden that is not occupied by the path?

📌 The dimensions of the garden excluding the path are reduced by 2 meters on each side:

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