Th scale factor of two similar cylinders is 3:4. What is the ratios of the areas in simplest form?

Question

hero · Answer

If the scale factor of two similar solids is a:b, then the ratio of their areas is a^2: b^2
In this case the scale factor of these are  3:4. Therefore the ratio of areas are 3^2: 4^2

hero · Answer

Therefore, if the scale factor of two similar cylinders is 3:4, then the ratio of their areas is 9:16

anonymous · Answer

9:16

anonymous · Answer

$$ 2\pi (3r)^2 + 2\pi (3r) (3h) : 2\pi (4r)^2 + 2\pi (4r) (4h)$$  
$$ 9 r^2 + 9rh : 16r^2 + 16rh$$
$$ 9 (r^2 + rh) : 16(r^2 + rh)$$
$$ 9  : 16$$

hero · Answer

Interesting approach

hero · Answer

Can you create a general formula for that approach?

anonymous · Answer

the general formula is dependant on the formula of the shape your dealing with 

for cylinder:
A=2πr 2 +2πrh

Sub each scale factor ratio into the equation (ie r -> (3r), h->(3h)), set as a ratio and reduce where you can.  cylinder worked out nice.  Is that kinda what you were after>