Question

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: the cost of a sheet for it, if a sheet measuring \[1\,{{m}^{2}}\] costs Rs. 20.

Answer 1

Hint: We should know that the area of cuboid is \[2lb+2bh+2lh\] and area of base is lb. For determining the cost of the sheet we need to first calculate the area of the sheet required keeping in mind that the box is open.

Complete step-by-step answer:

The length of the plastic box \[=l=1.5\,m\].
The breadth of the plastic box \[=b=1.5\,m\].
The depth of the plastic box \[=h=65\,cm=0.65\,m\].
Area of cuboid \[=2lb+2bh+2lh..........(1)\]
Area of base \[=lb......(2)\]
Putting values of \[l\], \[b\], \[h\] in equation (1) and equation (2) we get,
Area of cuboid \[=2\times 1.5\times 1.25+2\times 1.25\times 0.65+2\times 1.5\times 0.65\,=7.325\,{{m}^{2}}.....(3)\]
Area of base \[=lb=1.5\times 1.25=1.875\,{{m}^{2}}........(4)\]
Area of sheet required is area of cuboid minus area of base because the box is open, so subtracting equation (4) from equation (3) we get,
Area of sheet required \[=7.325-1.875=5.45\,{{m}^{2}}.......(5)\]
It is given in the question that the sheet measuring \[1\,{{m}^{2}}\]costs Rs. 20. So using this information we calculate the total cost of the sheet required.
Total cost of sheet required is cost per \[1\,{{m}^{2}}\]multiplied by area of sheet required and hence we get the total cost as,
\[\Rightarrow 5.45\,\times 20=109\]
Hence the total cost is Rs. 109.

Note: Knowing the area of cuboid is important and also here it is mentioned that the box is open which means one square face is not there and hence we subtract the area of base from the total area of cuboid to get the required area of sheet. We can make a mistake if we directly take depth as 65 as here in the question it is mentioned centimeter so we need to convert it into meters and then use it.