The surface areas of two similar solids are 384 yd squared and 1057 yd squared The volume of the larger solid is 1795. What is the volume of the smaller solid?

This is the concept of scale factors, we are required to calculate for the volume of the smaller solid if the larger solid has a volume of 1975.

Area scale factor = (linear scale factor) ^2

thus;

Area scale factor = (area of larger solid) / (area of smaller solid) = 1057/384

linear scale factor=√ (1057/384) = 5.7019

the volume scale factor = (linear scale factor) ^3=[volume of larger solid]/[volume of smaller solid]

The volume scale factor = (5.7019) ^3=185.3772

therefore;

volume of smaller solid=[volume of larger solid]/[volume scale factor]

=1795/185.3772

=9.683

The answer is 9.683 yd^3