Question

The diagonal of a cube joins two vertices not in same face. If the diagonals are 4 √3 cm long .What is the volume ?​

Answer 1

Answer:

64

Step-by-step explanation:

The diagonal of a cube made by joining opposite vertices is:

$\displaystyle d = \sqrt{a^2 + a^2 + a^2} = \sqrt{3a^2} = a\sqrt{3}$

$\displaystyle a\sqrt3 = 4\sqrt3$

∴ a = 4

Volume  = a³ = 64

See the image attached...

Answer 2

Step-by-step explanation:

Let the side =x

squaring both sides..

....$3 {x}^{2} = 16 \times 3 \\ 3 {x}^{2} = 48 \\ {x}^{2} = 16 \\ x = 4$volume =x×x×x

=4×4×4

64 cm cube