Find the height $ h $ of a cone if diameter $d = 46$ and volume $V = 22325$.
Answer
$h = 40.3002$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ d = 2 \cdot r $$After substituting $ d = 46 $ we have:
$$ 46 = 2 \cdot r $$ $$ r = \dfrac{ 46 }{ 2 } $$ $$ r = 23 $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = 22325 $ and $ r = 23 $ we have:
$$ 22325 = \dfrac{ 23 ^{ 2 } \cdot h \cdot \pi}{ 3 } $$$$ 22325 \cdot 3 = 23 ^{ 2 } \cdot h \cdot \pi $$$$ 66975 = 529 \cdot h \cdot \pi $$$$ h = \dfrac{ 66975 }{ 529 \, \pi} $$$$ h = 40.3002 $$This page was created using
Cone Calculator