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 base area $ AB $

To find base area $ AB $ use formula:

$$ AB = r^2 \cdot \pi $$

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

$$ AB = \left( 9\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 81\, \text{cm}^2 \cdot \pi $$

STEP 3: find lateral area $ AL $

To find lateral area $ AL $ use formula:

$$ AL = 2 \cdot h \cdot r \cdot \pi $$

After substituting $r = 9\, \text{cm}$ and $h = 19\, \text{cm}$ we have:

$$ AL = 38\, \text{cm} \cdot 9\, \text{cm} \cdot \pi $$$$ AL = 342\pi\, \text{cm}^2 $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = 2 AB + AL $$

After substituting $AB = 81\pi\, \text{cm}^2$ and $AL = 342\pi\, \text{cm}^2$ we have:

$$ A = 2 \cdot 81\pi\, \text{cm}^2 + 342\pi\, \text{cm}^2 $$ $$ A = 162\pi\, \text{cm}^2 + 342\pi\, \text{cm}^2 $$ $$ A = 504\pi\, \text{cm}^2 $$

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