The masses of two similar objects are 24kg and 81kg respectively. If the surface area of the larger object is 540 cm square, find the surface area of the smaller object.

Question

anonymous · Answer

ratio will be equall 
24/81=A/540

anonymous · Answer

Its wrong cause the answer will be 1822.5 and in the book the answer is 240

anonymous · Answer

Plus they are talking about masses and not lenghts

anonymous · Answer

The problem as stated is not a complete legitimate problem.  It can easily be proven that the dimensions (shape) of BOTH objects is necessary for computing both surface areas.  A formal proof can be given to validate this statement but a simple example will suffice.  Imagine an object that has 90 degree square corners and it is, say 1 x 1 x 100.  If you have double mass for the second object, you put 2 of these together.  You can put these together to get either 1 x 1 x 200 (end-to-end) or 1 x 2 x 100 (one on top of the other).  These two different looking objects have the same mass but a much different surface area.  Your problem definitely meant to include the shape of objects before and after.  Not enough information given to solve the problem.

anonymous · Answer

If, on the other hand, the problem stated that both objects were a cube or a sphere or a tetrahedron or a specific perfect solid, THEN you can relate mass to volume and then relate volume to surface area, ultimately relating mass to surface area and get your answer.  And it depends on what type of solid we are talking about.

anonymous · Answer

(24/81) = (8/27)^(2/3) = (2/3)^2 = (4/9) 
(4/9) * 540 = 240
ans: 240