Answer:
The surface area ratio of cylinder a to cylinder b is [tex]\frac{16}{9}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
The scale factor is equal to the ratio of its corresponding sides
so
Let
z------> the scale factor
x------> surface area of cylinder a
y------> surface area of cylinder b
[tex]z^{2}=\frac{x}{y}[/tex]
step 1
Find the scale factor
[tex]z=\frac{32}{24}=\frac{4}{3}[/tex]
step 2
Find the ratio of the surface areas
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{3}[/tex]
substitute
[tex](\frac{4}{3})^{2}=\frac{x}{y}[/tex]
[tex]\frac{x}{y}=\frac{16}{9}[/tex]
The surface area ration of Cylinder A to Cylinder B is 16:9
