Posted by Kat on .
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?
I am tearing my hair out over this question! Please help asap!

Math 
Reiny,
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 1^2 : 3^2 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