Find the height $ h $ of a cone if radius $r = \frac{ 1 }{ 3 }$ and volume $V = \frac{ 1 }{ 18 }$.
Answer
$h = 0.4775$
Explanation
To find height $ h $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = \frac{ 1 }{ 18 } $ and $ r = \frac{ 1 }{ 3 } $ we have:
$$ \frac{ 1 }{ 18 } = \dfrac{ \frac{ 1 }{ 3 } ^{ 2 } \cdot h \cdot \pi}{ 3 } $$$$ \frac{ 1 }{ 18 } \cdot 3 = \frac{ 1 }{ 3 } ^{ 2 } \cdot h \cdot \pi $$$$ \frac{ 1 }{ 6 } = \frac{ 1 }{ 9 } \cdot h \cdot \pi $$$$ h = \dfrac{ \frac{ 1 }{ 6 } }{ \frac{ 1 }{ 9 } \, \pi} $$$$ h = 0.4775 $$This page was created using
Cone Calculator