Question

the volume of solid A is 28m3 and the volume of solid B is 1,792m3. If the solids are similar, what is the ratio of the surface area of solid A to the surface area of solid B

Answer 1

if k is the scale factor between the dimensions of the similar solids, the areas are related by k² and the volumes are related by k³. That is

`\ \ (V_(a))/(V_(b))=k^(3)`

`\ \ k=((V_(a))/(V_(b)))^{(1)/(3)}`

The areas are related by k², so

`\ \ (A_(a))/(A_(b))=k^(2) = ((V_(a))/(V_(b)))^{(2)/(3)}`

`\ \ (A_(a))/(A_(b)) = ((28\ m^(3))/(1792\ m^(3)))^{(2)/(3)}=(4^(-3))^{(2)/(3)}`

`\ \ =4^(-2)=(1)/(16)`

The ratio of the surface area of solid A to that of solid B is ...
1/16