STEP 1: find side $ l $

To find side $ l $ use Pythagorean Theorem:

$$ r^2 + h^2 = l^2 $$

After substituting $r = \dfrac{\sqrt{ 6 }}{ 6 }\, \text{cm}$ and $h = 2\, \text{cm}$ we have:

$$ \left( \frac{\sqrt{ 6 }}{ 6 }\, \text{cm} \right)^{2} + \left( 2\, \text{cm} \right)^{2} = l^2 $$ $$ \frac{ 1 }{ 6 }\, \text{cm}^2 + 4\, \text{cm}^2 = l^2 $$ $$ l^2 = \frac{ 25 }{ 6 }\, \text{cm}^2 $$ $$ l = \sqrt{ \frac{ 25 }{ 6 }\, \text{cm}^2 } $$$$ l = \frac{ 5 \sqrt{ 6}}{ 6 }\, \text{cm} $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

$$ CSA = l \cdot r \cdot \pi$$

After substituting $r = \dfrac{\sqrt{ 6 }}{ 6 }\, \text{cm}$ and $l = \dfrac{ 5 \sqrt{ 6}}{ 6 }\, \text{cm}$ we have:

$$ CSA = \frac{ 5 \sqrt{ 6}}{ 6 }\, \text{cm} \cdot \frac{\sqrt{ 6 }}{ 6 }\, \text{cm} \cdot \pi$$$$ CSA = \frac{ 5 \sqrt{ 6}}{ 6 }\, \text{cm} \cdot \frac{\sqrt{ 6 }}{ 6 }\, \text{cm} \cdot \pi $$$$ CSA = \frac{ 5 }{ 6 }\pi\, \text{cm}^2 $$

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