Question

the ratio of the surface area of two solids is 9:1 and the ratio of their two volumes is also 9:1 your classmate concludes that the two solids are similar, with a scale factor of 9:1 explain and correct your classmates error

Answer 1

the volume scaling factor is in error

things you need to know

if the linear measurements are in a scaling factor if a:b

then the area's are in a scaling factor of a^2:b^2

and the volumes have a scaling factor of a^3:b^3

so if the area's have a factor of 9:1

then the linear is 3:1

so the volume should be 27:1

hope it helps