Find the height $ h $ of a cone if radius $r = 6$ and volume $V = 180\pi$.
Answer
$h = 15$
Explanation
To find height $ h $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = 180\pi $ and $ r = 6 $ we have:
$$ 180\pi = \dfrac{ 6 ^{ 2 } \cdot h \cdot \pi}{ 3 } $$$$ 180\pi \cdot 3 = 6 ^{ 2 } \cdot h \cdot \pi $$$$ 540\pi = 36 \cdot h \cdot \pi $$$$ h = \dfrac{ 540\pi }{ 36 \, \pi} $$$$ h = 15 $$This page was created using
Cone Calculator