Find the radius $ r $ of a cone if height $h = 18$ and volume $V = 678.584$.
Answer
$r = 6$
Explanation
To find radius $ r $ use formula:
$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$After substituting $ V = 678.584 $ and $ h = 18 $ we have:
$$ 678.584 = \dfrac{ r ^{ 2 } \cdot 18 \cdot \pi}{ 3 } $$$$ 678.584 \cdot 3 = r ^{ 2 } \cdot 18 \cdot \pi $$$$ 2035.752 = 18 \cdot r ^{ 2 } \cdot \pi $$$$ r ^{ 2 } = \dfrac{ 2035.752}{ 18 \, \pi } $$$$ r ^{ 2 } = 36 $$$$ r = \sqrt{ 36 } $$$$ r = 6 $$This page was created using
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