Find the area $ A $ of a cone if radius $r = 7$ and height $h = 24$.

$A = 224\pi$

STEP 1: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 7 $ we have:

$$ AB = 7^2 \cdot \pi $$ $$ AB = 49 \cdot \pi $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 7 $ and $ h = 24 $ we have:

$$ 7^2 + 24^2 = l^2 $$ $$ 49 + 576 = l^2 $$ $$ l^2 = 625 $$ $$ l = \sqrt{ 625 } $$$$ l = 25 $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 7 $ and $ l = 25 $ we have:

$$ CSA = 7 \cdot 25 \cdot \pi$$$$ CSA = 7 \cdot 25 \cdot \pi $$$$ CSA = 175\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 49\pi $ and $ CSA = 175\pi $ we have:

$$ A = 49\pi + 175\pi $$ $$ A = 49\pi + 175\pi $$ $$ A = 224\pi $$

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