Find the area $ A $ of a cone if radius $r = 2$ and height $h = 5$.

$A = 46.4024$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 2 $ we have:

$$ AB = 2^2 \cdot \pi $$ $$ AB = 4 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 2 $ and $ h = 5 $ we have:

$$ 2^2 + 5^2 = l^2 $$ $$ 4 + 25 = l^2 $$ $$ l^2 = 29 $$ $$ l = \sqrt{ 29 } $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 2 $ and $ l = \sqrt{ 29 } $ we have:

$$ CSA = 2 \cdot \sqrt{ 29 } \cdot \pi$$$$ CSA = 2 \cdot \sqrt{ 29 } \cdot \pi $$$$ CSA = 2 \sqrt{ 29 }\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 4\pi $ and $ CSA = 2 \sqrt{ 29 }\pi $ we have:

$$ A = 4\pi + 2 \sqrt{ 29 }\pi $$ $$ A = 4\pi + 2 \sqrt{ 29 }\pi $$ $$ A = 46.4024 $$

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