Questions & Answers

Question

Answers

Answer

Verified

129.3k+ views

Let us initially note down the dimensions of the matchbox,

Length if the matchbox is \[4cm\].

Width of the matchbox is \[2.5cm\].

Height of the matchbox is $1.5cm$.

When we visualize the matchbox with the above given dimensions, it looks like a cuboid.

Now, we need to find out the craft paper required in order to exactly cover the total outer surface of the matchbox.

It means clearly, we can say that the amount of craft paper required is exactly equal to the outer surface of the cuboid.

Outer surface has six faces with three pairs.

So, we need to find out the area of three rectangles with different dimensions and twice that as there are three more similar rectangles present.

And we are well familiar with the formula of total surface area of the cuboid also.

Total surface area of the cuboid is $2\left( {lb + bh + hl} \right)$ in square units.

Where $l$ is the length of the cuboid, $b$ is the width of the cuboid and $h$ is the height of the cuboid.

As we already have the values of $l$, $b$ and $h$ as \[4cm\], \[2.5cm\] and \[1.5cm\] respectively. Substitute the values in the formula to get the required solution.

Hence, the outer surface area of the matchbox $ = 2\left( {lb + bh + hl} \right)$

$

= 2\left( {4 \times 2.5 + 2.5 \times 1.5 + 1.5 \times 4} \right) \\

= 2\left( {10 + 3.75 + 6} \right) \\

= 2\left( {19.75} \right) \\

= 39.5c{m^2} \\

$

Therefore, we need $39.5c{m^2}$ of craft paper to cover the matchbox exactly.