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