The surface areas of two similar solids are 289 ft2 and 900 ft2. The volume of the larger solid is 1,755 ft3. What is the volume of the smaller solid?

Answer 1

the surface areas of two similar objects are proportional to the square of their sides

small side^2 / large side^2= 900/289
small side/large side = 30/17

volume of two similar objects is proportional to the cubes of their sides

smaller volume/1755 = 17^3/30^3
smaller volume = 1755(4913/27000) = appr 319

Answer 2

289 x 1755/900 = 563.55