Question
Find the height $ h $ of a cylinder if radius $r = 2\, \text{mm}$ and volume $V = 500\, \text{mm}^3$.
Answer
$8.9206\, \text{mm}$
Explanation
To find height $ h $ use formula:
$$ V = h ^{ 2 } \cdot r \cdot \pi$$After substituting $V = 500\, \text{mm}^3$ and $r = 2\, \text{mm}$ we have:
$$ 500\, \text{mm}^3 = 2\, \text{mm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 500\, \text{mm}^3}{ 2\, \text{mm} \, \pi } $$$$ h ^{ 2 } \approx 79.5773\, \text{mm}^2 $$$$ h \approx \sqrt{ 79.5773\, \text{mm}^2 } $$$$ h \approx 8.9206\, \text{mm} $$This page was created using
Cylinder Calculator