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

1. Hero

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

2. Hero

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

3. anonymous

9:16

4. anonymous

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

5. Hero

Interesting approach

6. Hero

Can you create a general formula for that approach?

7. anonymous

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>