Find the diameter $ d $ of a cone if height $h = 3\, \text{cm}$ and volume $V = 12.4\, \text{cm}$.

$2.6314\, \text{cm}^-1$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $V = 12.4\, \text{cm}$ and $h = 3\, \text{cm}$ we have:

$$ 12.4\, \text{cm} = \dfrac{ 3\, \text{cm} ^{ 2 } \cdot r \cdot \pi}{ 3 } $$$$ 12.4\, \text{cm} \cdot 3 = 3\, \text{cm} ^{ 2 } \cdot r \cdot \pi $$$$ 37.2\, \text{cm} = 9\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 37.2\, \text{cm} }{ 9\, \text{cm}^2 \, \pi} $$$$ r = 1.3157\, \text{cm}^-1 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $r = 1.3157\, \text{cm}^-1$ we have:

$$ d = 2 \cdot 1.3157\, \text{cm}^-1 $$ $$ d \approx 2.6314\, \text{cm}^-1 $$

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