Find the height $ h $ of a cone if diameter $d = 6$ and volume $V = 113.097$.
Answer
$h = 12$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ d = 2 \cdot r $$After substituting $ d = 6 $ we have:
$$ 6 = 2 \cdot r $$ $$ r = \dfrac{ 6 }{ 2 } $$ $$ r = 3 $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = 113.097 $ and $ r = 3 $ we have:
$$ 113.097 = \dfrac{ 3 ^{ 2 } \cdot h \cdot \pi}{ 3 } $$$$ 113.097 \cdot 3 = 3 ^{ 2 } \cdot h \cdot \pi $$$$ 339.291 = 9 \cdot h \cdot \pi $$$$ h = \dfrac{ 339.291 }{ 9 \, \pi} $$$$ h = 12 $$This page was created using
Cone Calculator