Answer:
The surface area of the second cylinder is equal to [tex]9.33\ m^{2}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then
the ratio of their surfaces areas is equal to the scale factor squared
Let
z-------> the scale factor
x------> the surface area of the smaller cylinder (second cylinder)
y-------> the surface area of the original cylinder (first cylinder)
so
[tex]z^{2}=\frac{x}{y}[/tex]
Step 1
Find the scale factor
[tex]z=\frac{2}{6}=\frac{1}{3}[/tex]
Step 2
Find the surface area of the second cylinder
we have
[tex]z=\frac{1}{3}[/tex]
[tex]y=84\ m^{2}[/tex]
substitute and solve for x
[tex](\frac{1}{3})^{2}=\frac{x}{84}[/tex]
[tex]x=\frac{1}{9}*84=9.33\ m^{2}[/tex]
