Find the diameter $ d $ of a cone if height $h = 8$ and volume $V = 150$.

$d = 23.9365$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $ V = 150 $ and $ h = 8 $ we have:

$$ 150 = \dfrac{ r ^{ 2 } \cdot 8 \cdot \pi}{ 3 } $$$$ 150 \cdot 3 = r ^{ 2 } \cdot 8 \cdot \pi $$$$ 450 = 8 \cdot r ^{ 2 } \cdot \pi $$$$ r ^{ 2 } = \dfrac{ 450}{ 8 \, \pi } $$$$ r ^{ 2 } = 143.2396 $$$$ r = \sqrt{ 143.2396 } $$$$ r = 11.9683 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $ r = 11.9683 $ we have:

$$ d = 2 \cdot 11.9683 $$ $$ d \approx 23.9365 $$

Cone Calculator