Find the radius $ r $ of a cone if height $h = 12$ and volume $V = 100$.
Answer
$r = 9.7721$
Explanation
To find radius $ r $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = 100 $ and $ h = 12 $ we have:
$$ 100 = \dfrac{ r ^{ 2 } \cdot 12 \cdot \pi}{ 3 } $$$$ 100 \cdot 3 = r ^{ 2 } \cdot 12 \cdot \pi $$$$ 300 = 12 \cdot r ^{ 2 } \cdot \pi $$$$ r ^{ 2 } = \dfrac{ 300}{ 12 \, \pi } $$$$ r ^{ 2 } = 95.493 $$$$ r = \sqrt{ 95.493 } $$$$ r = 9.7721 $$This page was created using
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