STEP 1: find side $ l $
To find side $ l $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 8 $ and $ h = 17 $ we have:
$$ 8^2 + 17^2 = l^2 $$ $$ 64 + 289 = l^2 $$ $$ l^2 = 353 $$ $$ l = \sqrt{ 353 } $$STEP 2: find Curved Surface Area $ CSA $
To find Curved Surface Area $ CSA $ use formula:
$$ CSA = r \cdot l \cdot \pi$$After substituting $ r = 8 $ and $ l = \sqrt{ 353 } $ we have:
$$ CSA = 8 \cdot \sqrt{ 353 } \cdot \pi$$$$ CSA = 8 \cdot \sqrt{ 353 } \cdot \pi $$$$ CSA = 8 \sqrt{ 353 }\pi $$