Find the lateral area $ AL $ of a cylinder if height $h = 20$ and volume $V = 1000$.
Answer
$AL = 713.6499\pi$
Explanation
STEP 1: find radius $ r $
To find radius $ r $ use formula:
$$ V = r ^{ 2 } \cdot h \cdot \pi$$After substituting $ V = 1000 $ and $ h = 20 $ we have:
$$ 1000 = 20 \cdot r ^{ 2 } \cdot \pi $$$$ r ^{ 2 } = \dfrac{ 1000}{ 20 \, \pi } $$$$ r ^{ 2 } = 318.3102 $$$$ r = \sqrt{ 318.3102 } $$$$ r = 17.8412 $$STEP 2: find lateral area $ AL $
To find lateral area $ AL $ use formula:
$$ AL = 2 \cdot r \cdot h \cdot \pi $$After substituting $ r = 17.8412 $ and $ h = 20 $ we have:
$$ AL = 35.6825 \cdot 20 \cdot \pi $$$$ AL = 713.6499\pi $$This page was created using
Cylinder Calculator