STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $d = 18\, \text{cm}$ we have:

$$ 18\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 18\, \text{cm} }{ 2 } $$ $$ r = 9\, \text{cm} $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $r = 9\, \text{cm}$ and $h = 12\, \text{cm}$ we have:

$$ \left( 9\, \text{cm} \right)^{2} + \left( 12\, \text{cm} \right)^{2} = l^2 $$ $$ 81\, \text{cm}^2 + 144\, \text{cm}^2 = l^2 $$ $$ l^2 = 225\, \text{cm}^2 $$ $$ l = \sqrt{ 225\, \text{cm}^2 } $$$$ l = 15\, \text{cm} $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $r = 9\, \text{cm}$ and $l = 15\, \text{cm}$ we have:

$$ CSA = 15\, \text{cm} \cdot 9\, \text{cm} \cdot \pi$$$$ CSA = 15\, \text{cm} \cdot 9\, \text{cm} \cdot \pi $$$$ CSA = 135\pi\, \text{cm}^2 $$

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