# 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.

Thus, its TSA = 6

*s*

^{2}where

*s*stands for side of the cube.

Since, this cube is without lid so we remove the area of its lid, that is,

*s*

^{2}from its TSA.

Thus, the area to be considered is 5

*s*

^{2}.

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

^{2}

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

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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