the area of the total surface of a polyhedron weighing 64 lb. is 340 sq. in. What is the surface of a similar polyhedron made of the same material and weighing 1000lb. ?

Answer 1

the ratio of the volumes (weight) of two similar figures is proportional to the cube of their sides
so the ratio of sides for the two solids
= cuberoot(1000/64) = 2.5

the ratio of the surface are is proportional to the square of their sides
so
x/340 = 2.5^2 / 1^2
x = 340(6.25) = 2125 square inches