Find the area $ A $ of a cone if diameter $d = 18$ and height $h = 12$.

$A = 216\pi$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $ d = 18 $ we have:

$$ 18 = 2 \cdot r $$ $$ r = \dfrac{ 18 }{ 2 } $$ $$ r = 9 $$

STEP 2: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 9 $ we have:

$$ AB = 9^2 \cdot \pi $$ $$ AB = 81 \cdot \pi $$

STEP 3: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 9 $ and $ h = 12 $ we have:

$$ 9^2 + 12^2 = l^2 $$ $$ 81 + 144 = l^2 $$ $$ l^2 = 225 $$ $$ l = \sqrt{ 225 } $$$$ l = 15 $$

STEP 4: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 9 $ and $ l = 15 $ we have:

$$ CSA = 9 \cdot 15 \cdot \pi$$$$ CSA = 9 \cdot 15 \cdot \pi $$$$ CSA = 135\pi $$

STEP 5: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 81\pi $ and $ CSA = 135\pi $ we have:

$$ A = 81\pi + 135\pi $$ $$ A = 81\pi + 135\pi $$ $$ A = 216\pi $$

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