Question

14. The square on the diagonal of a cube has an
area of 1875 sq. cm. Calculate :
(i) the side of the cube.
(ii) the total surface area of the cube.​

Answer 1

Answer:

let the edge of the cube be x cm.

We know, length of diagonal of the cube =

3

×(edge of the cube)

Therefore, length of diagonal of the cube =

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 = (

3

x)

2

cm

2

= 3x

2

cm

2

Therefore, 3x

2

=1875cm

2

....[given]

⇒x

2

=625cm

2

⇒x=25 cm

Edge of the cube = 25 cm

Answer 2

${\boxed{\underline{\orange{\bf\tt{Given:} } }}}$

The square on the diagonal of a cube has an

area of 1875 sq. cm.

${\boxed{\underline{\green{\bf\tt{To~Find :} } }}}$

(i) the side of the cube.

(ii) the total surface area of the cube.

${\boxed{\underline{\purple{\bf\tt{Solution:} } }}}$

i)

Let the side of the cube be m cm

Then the diagonal will be $\sqrt{3}m ~cm$

A/Q

The length of each side of the given square = diagonal= $\sqrt{3}m~cm$

Area of square= $(\sqrt{3}m)^2cm^2=3m^2cm^2$

$\sf \mapsto 3m^2=1875cm^2 \\\\\sf \mapsto m^2=\frac{1875}{3}=\frac{\cancel{1875}}{\cancel{3}}=625 \\\\\sf m=25cm$

Hence, the side of the cube is 25cm

ii)

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

$\mapsto6m^2 \mapsto6 \times 25^2 \\\\\sf 6 x 625=3750cm^2$