See explanation below.
Work Step by Step
Imagine that the solid is present as a cube of side 1cm. The surface area would be 6cm² The gas attacks this area during the reaction. Now imagine that you dissected the cube into 8 smaller cubes of side 0.5cm. Each cube would have an area of 1.5cm² and the total area would be increased to 12cm². Because the gas has this doubled area to attack the solid, the reaction rate would double. Take this to an extreme where you grind the cube into a fine powder. The total surface area would be extremely large, possibly measured in tens of square meters. The gas has this very high surface area to attack the solid, and so the reaction would proceed very rapidly.