Find the Curved Surface Area $ CSA $ of a cone if radius $r = 4$ and height $h = 8$.
Answer
$CSA = 16 \sqrt{ 5 }\pi$
Explanation
STEP 1: find side $ l $
To find side $ l $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 4 $ and $ h = 8 $ we have:
$$ 4^2 + 8^2 = l^2 $$ $$ 16 + 64 = l^2 $$ $$ l^2 = 80 $$ $$ l = \sqrt{ 80 } $$$$ l = 4 \sqrt{ 5 } $$STEP 2: 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 = 4 \sqrt{ 5 } $ we have:
$$ CSA = 4 \cdot 4 \sqrt{ 5 } \cdot \pi$$$$ CSA = 4 \cdot 4 \sqrt{ 5 } \cdot \pi $$$$ CSA = 16 \sqrt{ 5 }\pi $$This page was created using
Cone Calculator