Geometry
# Volume

Did the sphere have a greater surface area or does the cube?

**Useful equations:**

- Volume of a sphere: \(V=\frac{4}{3}\pi r^3\)
- Volume of a cube: \(V=a^3\)
- Surface area of a sphere: \(A=4\pi r^2\)
- Surface area of a cube: \(A=6a^2\)

What is the volume of the octahedron inside this \(8 \text{ in}^3\) cube?

A chocolate shop sells its products in 3 different shapes: a cylindrical bar, a spherical ball, and a cone. These 3 shapes are of the same height and radius, as shown in the picture. Which of these choices would give you the most chocolate?

\[\text{ I. A full cylindrical bar } \hspace{.4cm} \text{ or } \hspace{.45cm} \text{ II. A ball plus a cone }\]

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