Question

Find the area of cardboard required to prepare a closed box of dimensions \[12{\text{ }}cm \times 10{\text{ }}cm \times 8{\text{ }}cm.\]

Answer 1

Hint- In this question closed box dimensions are given, closed boxes always render the shape as cuboid so we will simply use the formula of total cuboid surface area to calculate the necessary area.

Complete step-by-step answer:
Closed box dimensions are
$
  l = 12cm \\
  b = 10cm \\
  h = 8cm \\
 $
As we know, the form of this closed box is always cuboid
Now to calculate the area of the cardboard we need to find the total surface area of the box or cuboid closed
As we know, the total cuboid surface area is given as
$2(lb + bh + hl)$
Where $l$ is the length , $b$is the breadth and $h$ is the height of cuboid.
Substitute all the given value in above formula we get
$
   = 2(12 \times 10 + 10 \times 8 + 8 \times 12) \\
   = 2(120 + 80 + 96) \\
   = 2(296) \\
   = 592c{m^2} \\
 $
Hence the area of cardboard is \[592{\text{ }}c{m^2}.\]

Note- A cuboid is a part of the 3D. Cuboids have six faces. More specifically, rectangular cuboids consist of $6$ rectangles, arranged at right angles. A cuboid that uses all faces in squares is a cube.