Find the area $ A $ of a cone if radius $r = 6$ and height $h = 8$.

$A = 96\pi$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 6 $ we have:

$$ AB = 6^2 \cdot \pi $$ $$ AB = 36 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 6 $ and $ h = 8 $ we have:

$$ 6^2 + 8^2 = l^2 $$ $$ 36 + 64 = l^2 $$ $$ l^2 = 100 $$ $$ l = \sqrt{ 100 } $$$$ l = 10 $$

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 $ and $ l = 10 $ we have:

$$ CSA = 6 \cdot 10 \cdot \pi$$$$ CSA = 6 \cdot 10 \cdot \pi $$$$ CSA = 60\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 36\pi $ and $ CSA = 60\pi $ we have:

$$ A = 36\pi + 60\pi $$ $$ A = 36\pi + 60\pi $$ $$ A = 96\pi $$

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