# 2 3D Geometry

1. A sphere is placed on an empty cube container with top open. The side of the cube is 8cm. Pull water to the container until the water touches the surface of the sphere. The depth of water is now 6cm. Ingoring the thickness of the container, what’s the volum of the sphere?

A. $$\frac{500 \pi}{3} cm^3$$ B. $$\frac{866 \pi}{3} cm^3$$ C. $$\frac{1372 \pi}{3} cm^3$$ D. $$\frac{2048 \pi}{3} cm^3$$

1. A tetrahedron’s vertexes $$S, A, B, C$$ are all on a sphere $$O$$. $$\triangle ABC$$ is an equalateral with side 1. $$SC$$ is a diameter of the sphere and it’s length is 2. What’s the volumn of the sphere?

2. A regular tetrahedron (all faces are equalateral) has side length $$\sqrt 2$$ and it’s vertexes are on a sphere, what’s the volumn of the sphere?

3. $$A,B,C,D$$ are four points on a sphere’s surface. The radius of the sphere is 4. $$\triangle ABC$$ is an equalateral with area $$9\sqrt 3$$, what’s the max volumn of tetrahedron DABC?