Find the area $ A $ of a cone if radius $r = 1.21$ and height $h = 3.8$.

$A = 6.2896$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 1.21 $ we have:

$$ AB = 1.21^2 \cdot \pi $$ $$ AB = 1.4641 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 1.21 $ and $ h = 3.8 $ we have:

$$ 1.21^2 + 3.8^2 = l^2 $$ $$ 1.4641 + 14.44 = l^2 $$ $$ l^2 = 15.9041 $$ $$ l = \sqrt{ 15.9041 } $$$$ l = 3.988 $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 1.21 $ and $ l = 3.988 $ we have:

$$ CSA = 1.21 \cdot 3.988 \cdot \pi$$$$ CSA = 1.21 \cdot 3.988 \cdot \pi $$$$ CSA = 4.8255\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 1.4641\pi $ and $ CSA = 4.8255\pi $ we have:

$$ A = 1.4641\pi + 4.8255\pi $$ $$ A = 1.4641 + 4.8255 $$ $$ A = 6.2896 $$

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