Question

The square on the diagonal of a cube has an area of $1875c{m}^2$. Calculate :
(i) the side of the cube,
(ii) the total surface area of the cube.

Answer 1

Given

Square of diagonals of cube $=1875c{m}^2$

Let $a$ be the side of cube

Then length of diagonals $=$ side of square $=\frac{\sqrt{3}a}{i}$

(i)

Given $\left(\sqrt{3}{a}^2\right)=1875$

$3a^2=1875$
$a^2=625$

$[a=25cm]$

Now side of cube $=25cm$

(ii)

Total surface area of cube $=6a^2$

$=6\times {25}^2$

$=6\times 625$

Area $3750c{m}^2$