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Kiya needs to cover a wooden box with a chart paper for her project. If the length, breadth and height of the box is 80cm, 40cm and 20cm respectively. How many square sheets of side 40cm would she require?

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Last updated date: 24th Feb 2024
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IVSAT 2024
Answer
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Hint: From the given data we conclude that Kiya wants to cover a cuboid box with square sheets. In order to cover the box we first need to find the total surface area of the box. And then the area of one square sheet. Because the number of square sheets required will be decided by the total surface area of the box she wants to cover for her project.

Formula used:
1. Number of square sheets required = \[\dfrac{{the{\text{ }}total{\text{ }}surface{\text{ }}area{\text{ }}of{\text{ }}the{\text{ }}box}}{{the{\text{ }}area{\text{ }}of{\text{ }}one{\text{ }}square{\text{ }}sheet.}}\]
2. Total surface area of the cuboid = \[2\left( {lb + bh + hl} \right)\]
3. Area of square = \[side \times side\]

Step by step solution:
First let’s find the total surface area of the cuboidal box Kiya wants to cover.
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Total surface area of the cuboid = \[2\left( {lb + bh + hl} \right)\]
Given that,
l=80cm, b=40cm and h=20cm
Putting these values,
\[{A_{cuboid box}} \Rightarrow 2\left( {80 \times 40 + 40 \times 20 + 20 \times 80} \right)\]
On multiplying,
\[ \Rightarrow 2\left( {3200 + 800 + 1600} \right)\]
\[ \Rightarrow 2 \times 5600\]
\[ \Rightarrow 11200c{m^2}\]
This is the total surface area of the box. Now let’s find the area of the sheet.
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We know that area of the square sheet is given by
Area of square = \[side \times side\]
Side of the square sheet is 40cm.
\[{A_{sheet}} \Rightarrow 40 \times 40\]
\[ \Rightarrow 1600c{m^2}\]
This is the area of the sheet.
Now the main task is to find the number of such sheets required.
Number of square sheets required = \[\dfrac{{the{\text{ }}total{\text{ }}surface{\text{ }}area{\text{ }}of{\text{ }}the{\text{ }}box}}{{the{\text{ }}area{\text{ }}of{\text{ }}one{\text{ }}square{\text{ }}sheet.}}\]
\[ \Rightarrow \dfrac{{11200}}{{1600}}\]
Cancelling the zeros
\[ \Rightarrow \dfrac{{112}}{{16}}\]
On dividing by 16 we get,
\[ \Rightarrow 7\]

This is the number of sheets required 7.

Note:
From the dimensions of the box we conclude that it is a cuboid box. Note that we have found the total surface area of the cuboid box because it is to be covered from all sides by the sheet paper. An area of sheet paper is calculated because it is to be covered on the box.
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