From a $25cm\times 35cm$ rectangular cardboard, an open box is to be made by cutting out identical square of area $25c{m}^2$, one from each corner and turning up the sides. The volume of the box is:

The correct option is B

$1875c{m}^3$

Dimensions of the cardboard: $25cm\times 35cm$

Area of the square that is cut out of the corner $=25c{m}^2$

$\Rightarrow$ Side of the square $=\sqrt{25}=5cm$

The cardboard with the square cut-outs is shown in the figure:

Length of box $=35-(5+5)=35-10=25cm$
Breadth of box $=25-(5+5)=25-10=15cm$
Height of box $=5cm$
Volume of box $=\text{Length}\times \text{Breadth}\times \text{Height}=25\times 15\times 5$
$=1875c{m}^3$