Find the area $ A $ of a cone if diameter $d = 24$ and slant height $l = 14$.

$A = 312\pi$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $ d = 24 $ we have:

$$ 24 = 2 \cdot r $$ $$ r = \dfrac{ 24 }{ 2 } $$ $$ r = 12 $$

STEP 2: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 12 $ we have:

$$ AB = 12^2 \cdot \pi $$ $$ AB = 144 \cdot \pi $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 12 $ and $ l = 14 $ we have:

$$ CSA = 12 \cdot 14 \cdot \pi$$$$ CSA = 12 \cdot 14 \cdot \pi $$$$ CSA = 168\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 144\pi $ and $ CSA = 168\pi $ we have:

$$ A = 144\pi + 168\pi $$ $$ A = 144\pi + 168\pi $$ $$ A = 312\pi $$

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