STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $d = 6\, \text{cm}$ we have:

$$ 6\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 6\, \text{cm} }{ 2 } $$ $$ r = 3\, \text{cm} $$

STEP 2: find base area $ AB $

To find base area $ AB $ use formula:

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

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

$$ AB = \left( 3\, \text{cm} \right)^{2} \cdot \pi $$ $$ AB = 9\, \text{cm}^2 \cdot \pi $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $r = 3\, \text{cm}$ and $l = 10\, \text{cm}$ we have:

$$ CSA = 10\, \text{cm} \cdot 3\, \text{cm} \cdot \pi$$$$ CSA = 10\, \text{cm} \cdot 3\, \text{cm} \cdot \pi $$$$ CSA = 30\pi\, \text{cm}^2 $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $AB = 9\pi\, \text{cm}^2$ and $CSA = 30\pi\, \text{cm}^2$ we have:

$$ A = 9\pi\, \text{cm}^2 + 30\pi\, \text{cm}^2 $$ $$ A = 9\pi\, \text{cm}^2 + 30\pi\, \text{cm}^2 $$ $$ A = 39\pi\, \text{cm}^2 $$

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