The ratio of surface area is equal to the ratio of the square of the corresponding dimensions. And ratio of volumes of two solids is equal to the cube of the ratio of the corresponding dimensions .
We start with the relation between ratio of surface area and ratio of corresponding sides. That is
[tex] \frac{340}{1158}=(\frac{x}{y} )^2 [/tex]
Here x and y are the corresponding sides .
[tex] \frac{x}{y} =\sqrt{\frac{340}{1158} } =0.542 [/tex]
Let the volume of the smaller one be v
[tex] \frac{v}{1712}=0.542^3 [/tex]
[tex] v=1712*0.542^3=272 [/tex]
So for the smaller solid, volume is 272 . And the correct option is the first option .
