Question

Find the area of cardboard required to prepare a closed box of dimension $12cm\times 10cm\times 8cm$

Answer 1

Hint: Area of cardboard required will be equal to total surface area of the closed box, and here the dimensions of box is like of a cuboid so here we will use the formula of total surface area of cuboid in order to calculate the the area of cardboard required to prepare a closed box, that is
Total Surface area of a cuboid \[=2\left[ \left( length\times breadth \right)+\left( breadth\times height \right)+\left( height\times length \right) \right]\]

Complete step-by-step answer:
Here we have dimension of box as,
Length $=12cm$ , Breadth$=10cm$ , Height$=8cm$

Now, in order to calculate the total surface area of the closed box, as the box is of the shape of a cuboid, we will use the formula of the cuboid that is,
Total Surface area of a cuboid \[=2\left[ \left( length\times breadth \right)+\left( breadth\times height \right)+\left( height\times length \right) \right]\],
 Substituting the known values from above and by using the above given formula we have,
$\begin{align}
  & \text{Total surface area of closed box}=2\left[ \left( 12\times 10 \right)+\left( 10\times 8 \right)+\left( 8\times 12 \right) \right]c{{m}^{2}} \\
 & \text{ }=2\left[ 120+80+96 \right]c{{m}^{2}} \\
 & \text{ }=2\left[ 296 \right]c{{m}^{2}} \\
 & \text{ }=592c{{m}^{2}} \\
\end{align}$
Hence, we have got the area of cardboard required to prepare a closed box of dimensions given above = Total Surface area of Box = $592c{{m}^{2}}$

Note: In order to calculate surface area or volume of any body, we should must observe the dimensions of the given body, like it is of the form of cube, cuboid or any other geometrical shape, so as to apply proper formula to it to get desired result. Also be careful while reading the question that what it is asking for, for example if it is asking about space occupied by the body then go for the calculation of volume of the body, whereas when it is asking for the area related to the body then go for the calculation of the total surface area or lateral surface area of the body according to the question asked.