Question
Find the radius $ r $ of a cone if height $h = 6\, \text{cm}$ and volume $V = 25\, \text{cm}$.
Answer
$0.6631\, \text{cm}^-1$
Explanation
To find radius $ r $ use formula:
$$ V = \dfrac{ h ^{ 2 } \cdot r \cdot \pi}{ 3 } $$After substituting $V = 25\, \text{cm}$ and $h = 6\, \text{cm}$ we have:
$$ 25\, \text{cm} = \dfrac{ 6\, \text{cm} ^{ 2 } \cdot r \cdot \pi}{ 3 } $$$$ 25\, \text{cm} \cdot 3 = 6\, \text{cm} ^{ 2 } \cdot r \cdot \pi $$$$ 75\, \text{cm} = 36\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 75\, \text{cm} }{ 36\, \text{cm}^2 \, \pi} $$$$ r = 0.6631\, \text{cm}^-1 $$This page was created using
Cone Calculator