Find the area $ A $ of a cone if radius $r = 6.1$ and height $h = 18.1$.

$A = 153.7216$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 6.1 $ we have:

$$ AB = 6.1^2 \cdot \pi $$ $$ AB = 37.21 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 6.1 $ and $ h = 18.1 $ we have:

$$ 6.1^2 + 18.1^2 = l^2 $$ $$ 37.21 + 327.61 = l^2 $$ $$ l^2 = 364.82 $$ $$ l = \sqrt{ 364.82 } $$$$ l = 19.1003 $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 6.1 $ and $ l = 19.1003 $ we have:

$$ CSA = 6.1 \cdot 19.1003 \cdot \pi$$$$ CSA = 6.1 \cdot 19.1003 \cdot \pi $$$$ CSA = 116.5116\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 37.21\pi $ and $ CSA = 116.5116\pi $ we have:

$$ A = 37.21\pi + 116.5116\pi $$ $$ A = 37.21 + 116.5116 $$ $$ A = 153.7216 $$

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