I've researched this question but explanations that I have found were either not thorough enough or simply seemed downright incorrect.
I thought it looked quite simple when I first saw it but it stumped me, Hopefully you can help me with this.
A and B are 2 shapes which are mathematically similar. The shapes are made from the same material.
The surface area of A is 50cm squared The surface area of B is 18cm squared
The mass of A is 500 grams
Calculate the mass of B
Thanks in advance :)
Mass is proportional to volume not surface area. In general surface area is proportional to the square of a linear measurement and volume is equal to the cube of a linear measurement. So volume is proportional to the 3/2 power of surface area. The ratio of areas is 50/18 so the ratio of volumes is $(50/18)^{3/2}= 4.63. Since A has mass 500 grams, B has mass 500/4.63= 108 grams.
(Actually, I am not convinced that "mathematically similar" means the objects have the same density.)