This is because the two types of molecule can only bump into each other at the liquid solid interface, i.e. on the surface of the solid. So the larger the surface area of the solid, the faster the reaction will be. Smaller particles have a bigger surface area than larger particle for the same mass of solid.

For a given mass of a solid, large lumps have smaller surface area to volume ratios than smaller lumps or powders. If a large lump is divided or ground into a powder: the area of exposed surface increases.

The large lump of CaCO3 has a small surface area relative to the same mass of powdered CaCO3. This means that more particles of CaCO3 will be in contact with HCl in the powdered CaCO3 than in the lumps. As a result, there can be more successful collisions per unit time and the reaction of powdered CaCO3 is faster.

For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is a ball, a consequence of the isoperimetric inequality in 3 dimensions.

Of all regular polygons with equal perimeter, the one with the most sides has the greatest area. A circle has a greater area than any regular polygon of the same perimeter. A sphere has a greater volume than solid figures with the same surface area.

icosahedron

A spherical shape is stable in one sense. Since every point on the surface is equidistant from the center of the sphere, which is the center of gravity, you place a sphere at any point it will be stable. Its the result of natural smaller forces of gravity, gradually putting pressure on a single point.

From the ISS, the distance to the horizon is over 1,000 miles. So from horizon to horizon, the section of the Earth you can see at any one time is a patch about 2,000 miles across, almost enough to see the entire United States at once.

A satellite in orbit around the earth cannot see half of the earth because of a simple geometric effect known as perspective.

The majority of satellites orbiting the Earth do so at altitudes between 160 and 2,000 kilometers. This orbital regime is called low Earth orbit, or LEO, due to the satellites’ relative closeness to the Earth. Satellites in LEO typically take between 90 minutes and 2 hours to complete one full orbit around the Earth.

Most satellites are the size of a small car (or smaller). They orbit the Earth at a distance that is at least 300 km (200 miles) from earth’s surface.

Currently the heaviest spacecraft is the International Space Station, nearly double Shuttle-Mir’s mass in orbit….Selected spacecraft (by mass)

Voyager 1

Voyager 1 is about 13 billion miles from Earth in interstellar space, and Voyager 2 is not far behind.