$A$ plastic box $1.5\, m$ long,$1.25\, m$ wide,and $65\, cm$ 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 the sheet for it,if a sheet measuring $1\, m^2$ costs $Rs. 20$.

(109) Given:
Length $(l) = 1.5\, m$
Breadth $(b) = 1.25\, m$
Depth $(h) = 65\, cm = 0.65\, m$
$(i)$ Since the box is open at the top,the area of the sheet required is the sum of the area of the four walls and the base:
Area $= 2lh + 2bh + lb$
$= [2 \times 1.5 \times 0.65 + 2 \times 1.25 \times 0.65 + 1.5 \times 1.25]\, m^2$
$= (1.95 + 1.625 + 1.875)\, m^2 = 5.45\, m^2$
$(ii)$ Cost of sheet per $m^2 = Rs. 20$
Total cost for $5.45\, m^2 = 5.45 \times 20 = Rs. 109$