Question

The surface area of a rectangular prism is 10.4 in2. What is the surface area of a similar prism that is larger by a scale factor of 3?

Answer 1

The surface areas of similar solids is proportional to the square of their sides 
since the ratio of sides is 1 : 3 
their surface areas have the ratio 1²: 3² or 1:9 
so the surface area is 9(10.4) or 93.6 

or 

original width = x 
original length = y 
original heigt = z 
original surface area = 2(xy) + 2(xz) + 2(yz) 
= 2(xy + xz + yz) 

new width = 3x 
new length = 3y 
new height = 3z 
new surface area = 2(9xy) + 2(9xz) + 2(9yz) 
= 18(xy + xz + yz) 

ratio of new to old = 18(xy + xz + yz) : 2(xy + xz + yz) 
= 9:1