Asked by sara
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. ?
Answers
Answered by
Reiny
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
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
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