A plastic box $ 1.5 \mathrm{~m} $ long. $ 1.25 \mathrm{~m} $ wide and $ 65 \mathrm{~cm} $ deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring $ 1 \mathrm{~m}^{2} $ costs $ \mathrm{Rs.} 20 $.

Given:

The length of the box $=1.5\ m$.

The breadth of the box $=1.25\ m$.

The height of the box $=65\ cm=0.65\ m$.

To do:

We have to find:

(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring \( 1 \mathrm{~m}^{2} \) costs Rs. 20.

Solution:

(i) Area of the sheet required $=2lb+2bh+2lh−lb$  (It is open at the top) 

$=lb+2lh+2bh$

$=(1.5\times1.25)+2(1.5\times0.65)+2(1.25\times0.65)$ 

$=(1.875+1.95+1.625)$

$=5.45\ m^2$

ii) Cost of the sheet per square metre$= Rs.\ 20$.

Cost of sheet of $5.45\ m^2 = Rs.\ 5.45\times20$

$=Rs.\ 109$.