STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $r = 2\, \text{cm}$ we have:

$$ AB = \left( 2\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 4\, \text{cm}^2 \cdot \pi $$

STEP 2: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $r = 2\, \text{cm}$ and $l = 3\, \text{cm}$ we have:

$$ CSA = 3\, \text{cm} \cdot 2\, \text{cm} \cdot \pi$$$$ CSA = 3\, \text{cm} \cdot 2\, \text{cm} \cdot \pi $$$$ CSA = 6\pi\, \text{cm}^2 $$

STEP 3: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $AB = 4\pi\, \text{cm}^2$ and $CSA = 6\pi\, \text{cm}^2$ we have:

$$ A = 4\pi\, \text{cm}^2 + 6\pi\, \text{cm}^2 $$ $$ A = 4\pi\, \text{cm}^2 + 6\pi\, \text{cm}^2 $$ $$ A = 10\pi\, \text{cm}^2 $$

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