Question
Find the diameter $ d $ of a cylinder if height $h = 7\, \text{cm}$ and volume $V = 175\pi\, \text{cm}$.
Answer
$\dfrac{ 50 }{ 7 }\, \text{cm}^-1$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ V = h ^{ 2 } \cdot r \cdot \pi $$After substituting $V = 175\pi\, \text{cm}$ and $h = 7\, \text{cm}$ we have:
$$ 175\pi\, \text{cm} = 49\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 175\pi\, \text{cm} }{ 49\, \text{cm}^2 \, \pi} $$$$ r = \frac{ 25 }{ 7 }\, \text{cm}^-1 $$STEP 2: find diameter $ d $
To find diameter $ d $ use formula:
$$ d = 2 \cdot r $$After substituting $r = \dfrac{ 25 }{ 7 }\, \text{cm}^-1$ we have:
$$ d = 2 \cdot \frac{ 25 }{ 7 }\, \text{cm}^-1 $$ $$ d = \frac{ 50 }{ 7 }\, \text{cm}^-1 $$This page was created using
Cylinder Calculator