Find the face diagonal $ f $ of a cube if face area $FA = 6\, \text{cm}$.
Answer
$2 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
After substituting $FA = 6\, \text{cm}$ we have:
$$ FA = a^2 $$ $$ a^2 = 6\, \text{cm} $$ $$ a = \sqrt{ 6\, \text{cm} } $$STEP 2: find face diagonal $ f $
To find face diagonal $ f $ use formula:
$$ f = \sqrt{ 2 } \cdot a $$After substituting $a = \sqrt{ 6 }\, \text{cm}^0$ we have:
$$ f = \sqrt{ 2 } \cdot \sqrt{ 6 } $$ $$ f = 2 \sqrt{ 3 } $$This page was created using
Cube Calculator