Question

Suman made a cardboard box in the form of a cube without a lid. If the total surface area of the box was 180 sq.cm, what are the dimensions of the box?

Answer 1

Hint: For solving this question you should know about the area of a square. We solve this problem by determining the surface area of a cube. But this is already given to us, so we will determine the sides of this cube by using the formula of the area of the cube. The surface area of a cube is equal to the square of it’s any side. Here the surface area formula will be used to find the side of this cube.

Complete step by step answer:
According to the question, the surface area of a cube is given to us and we are asked to find the dimensions of this cube. We are given that a cardboard box is to be made in the form of a cubic box and the area of the cardboard is $180c{{m}^{2}}$. Let us consider the sides of the cardboard are $a$ and make a diagram for it, then we have,

As we know that the area of a square is calculated by ${{\left( side \right)}^{2}}$, and the cube’s all sides are of equal length. But here the cube has no lid, so the total area of the cube is $5{{a}^{2}}$,
$\begin{align}
  & \Rightarrow 5{{a}^{2}}=180c{{m}^{2}} \\
 & \Rightarrow {{a}^{2}}=\dfrac{180}{5}=36c{{m}^{2}} \\
 & \Rightarrow side=6cm \\
\end{align}$
Therefore the dimensions of the box $=6\times 6\times 6$.

Note: While solving these types of questions you have to keep in mind that all the sides of a cube are always equal with each other and these are also the same in a square. But in a rectangle only opposite sides are equal to each other and all the angles are at right angles.