Find the height $ h $ of a cone if diameter $d = 16$ and slant height $l = 20$.
Answer
$h = 4 \sqrt{ 21 }$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ d = 2 \cdot r $$After substituting $ d = 16 $ we have:
$$ 16 = 2 \cdot r $$ $$ r = \dfrac{ 16 }{ 2 } $$ $$ r = 8 $$STEP 2: find side $ h $
To find side $ h $ use Pythagorean Theorem:
$$ r^2 + h^2 = l^2 $$After substituting $ r = 8 $ and $ l = 20 $ we have:
$$ 8^2 + h^2 = 20^2 $$ $$ h^2 = 20^2 - 8^2 $$ $$ h^2 = 400 - 64 $$ $$ h^2 = 336 $$ $$ h = \sqrt{ 336 } $$$$ h = 4 \sqrt{ 21 } $$This page was created using
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