Question

A right cylinder has a radius of 6 m and a surface area of 84 m². Find the surface area of a similar cylinder with a radius of 2 m.

Answer 1

Answer:

The surface area of the second cylinder is equal to $9.33\ m^{2}$

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

$z^{2}=\frac{x}{y}$

Step 1

Find the scale factor

$z=\frac{2}{6}=\frac{1}{3}$

Step 2

Find the surface area of the second cylinder

we have

$z=\frac{1}{3}$

$y=84\ m^{2}$

substitute and solve for x

$(\frac{1}{3})^{2}=\frac{x}{84}$

$x=\frac{1}{9}*84=9.33\ m^{2}$