Find the height $ h $ of a cone if volume $V = 7762392$ and base area $AB = 484$.

$h = 48114.1125$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

After substituting $ AB = 484 $ we have:

$$ AB = r^2 \cdot \pi $$ $$ r^2 \cdot \pi = 484 $$ $$ r = \sqrt{ \frac{ 484 }{\pi} } $$ $$ r \approx 12.4122 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $ V = 7762392 $ and $ r = 12.4122 $ we have:

$$ 7762392 = \dfrac{ 12.4122 ^{ 2 } \cdot h \cdot \pi}{ 3 } $$$$ 7762392 \cdot 3 = 12.4122 ^{ 2 } \cdot h \cdot \pi $$$$ 23287176 = 154.0616 \cdot h \cdot \pi $$$$ h = \dfrac{ 23287176 }{ 154.0616 \, \pi} $$$$ h = 48114.1125 $$

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