Only the particles on the outside of a solid can meet the other reactant. The surface area to volume ratio tells you how much surface there is for each unit of volume. A larger ratio means more of the solid is exposed.
Take a cube with sides of 1 cm. It has six faces, each 1 cm2, so its surface area is 6 cm2 and its volume is 1 cm3. The ratio is 6:1. A cube with sides of 2 cm has a surface area of 24 cm2 and a volume of 8 cm3, so its ratio is 3:1. The smaller cube has the larger ratio.
Cutting a solid into smaller pieces keeps the mass the same but increases the total surface area. The surface area to volume ratio is larger, so more particles of the solid are exposed to the reactant. This makes collisions more frequent, so the rate of reaction is faster. This is why a powder reacts faster than lumps.
