Question
Find the base area $ A_B $ of a cylinder if height $h = 20\, \text{cm}$ and volume $V = 1000\, \text{cm}$.
Answer
$0.6333\pi\, \text{cm}^-2$
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 base area $ AB $
To find base area $ AB $ use formula:
$$ AB = r^2 \cdot \pi $$After substituting $r = 0.7958\, \text{cm}^-1$ we have:
$$ AB = \left( 0.7958\, \text{cm}^-1 \right)^{2} \cdot \pi $$ $$ AB = 0.6333\, \text{cm}^-2 \cdot \pi $$This page was created using
Cylinder Calculator