Find the height $ h $ of a cone if radius $r = 3$ and volume $V = 27\pi$.
Answer
$h = 9$
Explanation
To find height $ h $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = 27\pi $ and $ r = 3 $ we have:
$$ 27\pi = \dfrac{ 3 ^{ 2 } \cdot h \cdot \pi}{ 3 } $$$$ 27\pi \cdot 3 = 3 ^{ 2 } \cdot h \cdot \pi $$$$ 81\pi = 9 \cdot h \cdot \pi $$$$ h = \dfrac{ 81\pi }{ 9 \, \pi} $$$$ h = 9 $$This page was created using
Cone Calculator