Question

The square on the diagonal of a cube has an area of $1857$ sq. cm. Calculate the total surface area of the cube.

Answer 1

Let side of cube be $a$ cm
Length of its diagonal
$L_d=a\sqrt{3}$
Area $=A={\left(a\sqrt{3}\right)}^2$
$\therefore 1875={\left(a\sqrt{3}\right)}^2$
$\therefore a=25$
$\therefore$ surface area $=6\times 25\times 25$
$=3750{cm}^2$