Find the area $ A $ of a cone if diameter $d = 6$ and slant height $l = 10$.

$A = 39\pi$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $ d = 6 $ we have:

$$ 6 = 2 \cdot r $$ $$ r = \dfrac{ 6 }{ 2 } $$ $$ r = 3 $$

STEP 2: find base area $ AB $

To find base area $ AB $ use formula:

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

After substituting $ r = 3 $ we have:

$$ AB = 3^2 \cdot \pi $$ $$ AB = 9 \cdot \pi $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 3 $ and $ l = 10 $ we have:

$$ CSA = 3 \cdot 10 \cdot \pi$$$$ CSA = 3 \cdot 10 \cdot \pi $$$$ CSA = 30\pi $$

STEP 4: find area $ A $

To find area $ A $ use formula:

$$ A = AB + CSA $$

After substituting $ AB = 9\pi $ and $ CSA = 30\pi $ we have:

$$ A = 9\pi + 30\pi $$ $$ A = 9\pi + 30\pi $$ $$ A = 39\pi $$

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