Proportional Reasoning

Question

Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the sphere weigh?

Answer 1

surface area ratio is the square of linear ratio, so that is 2:3

 

volume ratio is the cube of the above, i.e. 8:27

 

so the weight of the larger must be (27/8)(10 kg).