Question

The square on the diagonal of a cube has an area of $1875$ sq. cm Calculate the side of the cube.

• A. $25$ cm
• B. $24$ cm
• C. $21$ cm
• D. $20$ cm

Answer 1

The correct option is A $25$ cm

Let the edge of the cube be $x$ cm.
We know, length of diagonal of the cube $=$ $\sqrt{3}\times ($edge of the cube$)$
Therefore, length of diagonal of the cube $=$ $\sqrt{3}x$ cm.
The side of the square is equal to the length of diagonal of the cube.
Area of square drawn on diagonal of the cube $=$ $(\sqrt{3}x{)}^{2}c{m}^2$
$=$ $3x^{2}c{m}^2$
Therefore, $3x^2=1875c{m}^2$ ....[given]
$\Rightarrow x^2=625c{m}^2$
$\Rightarrow x=25$ cm
Edge of the cube $=$ $25$ cm