What is the ratio of the surface area of the enlarged prism to the surface area of the original prism

Question

A right rectangular prism is enlarged by a scale factor of 7. What is the ratio of the surface area of the enlarged prism to the surface area of the original prism with a length of 5 inches, height of 4 inches, and a width of 3 inches? *

Answer 1

Surface area of original prism = 2(3·5) + 2(3·4) + 2(5·4) = 94

 

Dimensions of enlarged prism:  width = 21, length = 35, height = 28

 

Surface area of enlarged prism = 2(21·35) + 2(21·28) + 2(35·28)

 

                                              = 4606

 

                                              = (49)(94) = 7²(94)

 

Ratio of surface areas of the two prisms = 49/1 

Answer 2

The surface area will be proportional to the square of the scale factor, i.e. 49.