Answering
Ratio of surface areas is equal to the square of the corresponding dimensions and ratio of volumes of the two solids is equal to the cube of the ratio of the dimensions of the two solids .
Using that information , and let a and b are the corresponding sides of the two solids , we will get
Now we need to get rid of the square. And for that, we take square root to both sides,
\sqrt{\frac{311}{1037}}=\frac{a}{b}
Let the volume of the smaller solid be x .
So we will get
\frac{x}{1755}=(\sqrt{\frac{311}{1037}} )^3
x = 1755(\sqrt{\frac{311}{1037}})^3
x=288 ft approx
So the volume of the smaller solid = 288 ft approx