Find the area $ A $ of a cone if radius $r = 12$ and height $h = 14$.

$A = 1147.5266$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 12 $ we have:

$$ AB = 12^2 \cdot \pi $$ $$ AB = 144 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 12 $ and $ h = 14 $ we have:

$$ 12^2 + 14^2 = l^2 $$ $$ 144 + 196 = l^2 $$ $$ l^2 = 340 $$ $$ l = \sqrt{ 340 } $$$$ l = 2 \sqrt{ 85 } $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 12 $ and $ l = 2 \sqrt{ 85 } $ we have:

$$ CSA = 12 \cdot 2 \sqrt{ 85 } \cdot \pi$$$$ CSA = 12 \cdot 2 \sqrt{ 85 } \cdot \pi $$$$ CSA = 24 \sqrt{ 85 }\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 144\pi $ and $ CSA = 24 \sqrt{ 85 }\pi $ we have:

$$ A = 144\pi + 24 \sqrt{ 85 }\pi $$ $$ A = 144\pi + 24 \sqrt{ 85 }\pi $$ $$ A = 1147.5266 $$

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