Find the volume $ V $ of a cube if body diagonal $d = 5 \sqrt{ 3 }$.
Answer
$V = 125$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 3 } \cdot a $$After substituting $ d = 5 \sqrt{ 3 } $ we have:
$$ 5 \sqrt{ 3 } = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ 5 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a = 5 $$STEP 2: find volume $ V $
To find volume $ V $ use formula:
$$ V = a^3 $$After substituting $ a = 5 $ we have:
$$ V = 5^3 $$ $$ V = 125 $$This page was created using
Cube Calculator