Question

The length of Diagonel of a cube is 10 root 2...what is the volume of the cube ?

Answer 1

hello users......

we have given that:-
diagonal of cube = 10√2

we have to find :-
volume of cube =?

solution:-
we know that:
diagonal of cube = a ×√3
and
volume of cube = a³

Here,
a√3 = 10√2
=> a= 10√2 / √3

now,
volume of cube = a³
=> (10√2 / √3 ) ³
= 10³× √2³ / √3³
= 1000 × 2√2 / 3√3
=> 2000√2 / 3√3

=> (2000× √2 × 3√3) / (3√3 ×3√3)
( multiple & divide by 3√3 )

=> 6000√6 / 27

=> 2000√6 / 9 unit³ answer

⭐✡ hope it helps✡⭐