Question

A metal sheet of width $1m$ is kept in a roll. A worker needs to make a box of dimensions $50cm\times 30cm\times 45cm$. Find the length of the sheet required to make the box.

• A. $1m$
• B. $1.02m$
• C. $112cm$
• D. $95cm$

Answer 1

The correct option is B

$1.02m$

From the given dimensions of the box, we may conclude that the box is cuboid-shaped.
Total area of the metal sheet required
= TSA of the box
= $2(lb+bh+hl)$
Given,
$\text{Length,}l=50\text{cm}\text{Breadth,}b=30\text{cm}\text{Height,}h=45\text{cm}$

$\therefore \text{Total Surface Area}=2(50\times 30+30\times 45+45\times 50)$
$=2(1500+1350+2250)$
$=2\left(5100\right)$
$=10,200c{m}^2$

Given, width of the sheet = 1 m = 100 cm.

Since, Area of sheet = TSA of the box, we have
$\text{length}\times \text{width}=10200c{m}^2$
$\Rightarrow \text{length}=\frac{10200c{m}^2}{\text{width}}$
$\Rightarrow \text{length}=\frac{10200c{m}^2}{100cm}$
$\Rightarrow \text{length}=102cm$
$\Rightarrow \text{length}=1.02m$

Hence, the length of the metal sheet required to make the box is $1.02m$.