Question
Find the lateral area $ AL $ of a cylinder if height $h = 20\, \text{cm}$ and volume $V = 1000\, \text{cm}$.
Answer
$31.831\pi$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ V = h ^{ 2 } \cdot r \cdot \pi $$After substituting $V = 1000\, \text{cm}$ and $h = 20\, \text{cm}$ we have:
$$ 1000\, \text{cm} = 400\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 1000\, \text{cm} }{ 400\, \text{cm}^2 \, \pi} $$$$ r = 0.7958\, \text{cm}^-1 $$STEP 2: find lateral area $ AL $
To find lateral area $ AL $ use formula:
$$ AL = 2 \cdot h \cdot r \cdot \pi $$After substituting $r = 0.7958\, \text{cm}^-1$ and $h = 20\, \text{cm}$ we have:
$$ AL = 40\, \text{cm} \cdot 0.7958\, \text{cm}^-1 \cdot \pi $$$$ AL = 31.831\pi $$This page was created using
Cylinder Calculator