Find the area $ A $ of a cone if radius $r = 4$ and height $h = \sqrt{ 273 }$.

$A = 84\pi$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 4 $ we have:

$$ AB = 4^2 \cdot \pi $$ $$ AB = 16 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 4 $ and $ h = \sqrt{ 273 } $ we have:

$$ 4^2 + \left( \sqrt{ 273 } \right)^{ 2 } = l^2 $$ $$ 16 + 273 = l^2 $$ $$ l^2 = 289 $$ $$ l = \sqrt{ 289 } $$$$ l = 17 $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 4 $ and $ l = 17 $ we have:

$$ CSA = 4 \cdot 17 \cdot \pi$$$$ CSA = 4 \cdot 17 \cdot \pi $$$$ CSA = 68\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 16\pi $ and $ CSA = 68\pi $ we have:

$$ A = 16\pi + 68\pi $$ $$ A = 16\pi + 68\pi $$ $$ A = 84\pi $$

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