Find the diameter $ d $ of a cone if height $h = 13$ and volume $V = 510$.

$d = 44.1368$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$

After substituting $ V = 510 $ and $ h = 13 $ we have:

$$ 510 = \dfrac{ r ^{ 2 } \cdot 13 \cdot \pi}{ 3 } $$$$ 510 \cdot 3 = r ^{ 2 } \cdot 13 \cdot \pi $$$$ 1530 = 13 \cdot r ^{ 2 } \cdot \pi $$$$ r ^{ 2 } = \dfrac{ 1530}{ 13 \, \pi } $$$$ r ^{ 2 } = 487.0145 $$$$ r = \sqrt{ 487.0145 } $$$$ r = 22.0684 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $ r = 22.0684 $ we have:

$$ d = 2 \cdot 22.0684 $$ $$ d \approx 44.1368 $$

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