# suman made a cardboard box in the form of a cube without a lid. if the total surface area of this box was 180 sq.cm, what are the dimensions.

Since the cardboard box is a cube.

Thus, its TSA = 6s2 where s stands for side of the cube.

Since, this cube is without lid so we remove the area of its lid, that is, s2 from its TSA.

Thus, the area to be considered is 5s2.

Also, we are given that surface area of the box without lid = 180 cm2

$⇒5{s}^{2}=180\phantom{\rule{0ex}{0ex}}⇒{s}^{2}=36\phantom{\rule{0ex}{0ex}}⇒s=\sqrt{36}\phantom{\rule{0ex}{0ex}}⇒s=±6$

We reject the negative value as length of the cubical box cannot be negative.

Thus, side of the box = 6 cm

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