Question

A sweet shop was placing an order for making cardboard boxes of packing their sweet two size of boxes one $20cm\times 15cm\times 5cm$ and the other $12cm\times 10cm\times 5cm$ were required for all the overlaps $5\%$ of the total surface area is required extra. If the cost of the cardboards is $Rs.4.50$ per $1000c{m}^2$, find the cost of cardboard required for supplying $100$ boxes of each kind.

Answer 1

The dimension of bigger box is $15\times 20\times 5$.

The outer surface area $=2(15\times 20+20\times 5+5\times 15)=950$ cm square

The area of extra sheet $=5\%$ of $950=950\times \left(\frac{5}{100}\right)=47.5$

The total area of cardboard required for bigger box $=950+47.5=997.5$ cm square

The dimension of smaller box is $10\times 12\times 5$.

The outer surface area $=2(10\times 12+12\times 5+5\times 10)=460$ cm square

The area of extra sheet $=5\%$ of $460=460\times \left(\frac{5}{100}\right)=23$

The total area of cardboard required for bigger box $=460+23=483$ cm square

For $250$ boxes of each kind required cardboard $=100\times (997.5+483)=100\times 1480.5=148050$ cm square

Cost of the card board $=148050\times \left(\frac{4.5}{1000}\right)=Rs.666.225$