Find the area $ A $ of a cone if radius $r = 10$ and height $h = 24$.

$A = 360\pi$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 10 $ we have:

$$ AB = 10^2 \cdot \pi $$ $$ AB = 100 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 10 $ and $ h = 24 $ we have:

$$ 10^2 + 24^2 = l^2 $$ $$ 100 + 576 = l^2 $$ $$ l^2 = 676 $$ $$ l = \sqrt{ 676 } $$$$ l = 26 $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 10 $ and $ l = 26 $ we have:

$$ CSA = 10 \cdot 26 \cdot \pi$$$$ CSA = 10 \cdot 26 \cdot \pi $$$$ CSA = 260\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 100\pi $ and $ CSA = 260\pi $ we have:

$$ A = 100\pi + 260\pi $$ $$ A = 100\pi + 260\pi $$ $$ A = 360\pi $$

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