Geometry
# Surface Area

In a spherical ball, a large number of dimples have been carved. The shape of these dimples is part of a sphere.

Is it possible for the dimpled ball to have a *smaller* surface area than it had before the dimples were carved?

Two equivalent regular hexagonal-based prisms are divided and rearranged into 3 equilateral triangular-based prisms, as shown above. After rearrangement, the total surface area of all prisms has increased by 12.5% with the constant height.

If the height of each prism is \(\sqrt{3} \text{ cm}\), what is the side length of the regular hexagon base in \(\text{cm}\)?

A spherical orange is cut about the vertical axis into 8 equal slices as shown above.

What is the ratio of the total surface area of the 8 slices to that of the original orange?

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