Find the Curved Surface Area $ CSA $ of a cone if diameter $d = 8$ and height $h = 17$.

$CSA = 4 \sqrt{ 305 }\pi$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $ d = 8 $ we have:

$$ 8 = 2 \cdot r $$ $$ r = \dfrac{ 8 }{ 2 } $$ $$ r = 4 $$

STEP 2: find side $ l $

To find side $ l $ use Pythagorean Theorem:

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

After substituting $ r = 4 $ and $ h = 17 $ we have:

$$ 4^2 + 17^2 = l^2 $$ $$ 16 + 289 = l^2 $$ $$ l^2 = 305 $$ $$ l = \sqrt{ 305 } $$

STEP 3: find Curved Surface Area $ CSA $

To find Curved Surface Area $ CSA $ use formula:

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

After substituting $ r = 4 $ and $ l = \sqrt{ 305 } $ we have:

$$ CSA = 4 \cdot \sqrt{ 305 } \cdot \pi$$$$ CSA = 4 \cdot \sqrt{ 305 } \cdot \pi $$$$ CSA = 4 \sqrt{ 305 }\pi $$

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