Question

Vishal wishes to cover a box of size 80 cm x 40 cm x 20 cm using a square sheet of paper is $40{\text{ c}}{{\text{m}}^2}$. Find the number of sheet needed to cover the box.

Answer 1

Hint: In this question, we need to evaluate the number of sheet needed to cover the box such that Vishal wishes to cover a box of size 80 cm x 40 cm x 20 cm using a square sheet of paper is $40{\text{ c}}{{\text{m}}^2}$. For this, we will first calculate the total surface area of the box and then divide it by the area of the sheet to find the number of sheets of the same size required to cover the box.

Complete step-by-step answer:
Given that,
Length of the box \[l = 80\;cm\]
Breadth of the box \[b = 40\;cm\]
Height of the box \[h = 20\;cm\]
Total surface area of the cuboid is given by the formula
 \[\Rightarrow SA = 2\left( {lb + bh + hl} \right)\] , where l is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid.
Now, since we need to find the number of sheet needed to cover the box we will first we will find the total surface area of the box using the formula
 \[\Rightarrow SA = 2\left( {lb + bh + hl} \right)\]
Substitute the value given dimension of the box in the above formula
 \[
\Rightarrow SA = 2\left( {80 \times 40 + 40 \times 20 + 20 \times 80} \right) \\
   = 2\left( {3200 + 800 + 1600} \right) \\
   = 2\left( {5600} \right) \\
   = 11200\;c{m^2} \;
 \]
Hence the total surface area of the box is
 \[ = 11200\;c{m^2}\]
Now we need to find the total number of sheet needed of the given area $40{\text{ c}}{{\text{m}}^2}$ to cover the box by dividing the total surface area of the box by the area of each sheet
Therefore the total number of the sheet required to cover the box
 \[ = \dfrac{{11200}}{{40}} = 280\]
Hence, the sheet required is \[ = 280\]
So, the correct answer is “280”.

Note: Number of sheet required of area $40{\text{ c}}{{\text{m}}^2}$ will cover the whole box through the surface and this 280 numbers of sheet will totally cover the box of size 80 cm x 40 cm x 20 cm. If we add the area of the total 280 sheets then this area will be equal to the surface area of the box.
\[
  280 \times 40 = 2\left( {80 \times 40 + 40 \times 20 + 20 \times 80} \right) \\
   \Rightarrow 11200 = 11200 \\
 \]