Question

Shanti sweets stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25cm\times 20cm\times 5cm$ and the smaller of dimension \[15cm\times 12cm\times 5cm\]. For all the overlaps, 5% of the total surface is required extra. If the cost of the cardboard is $Rs.4$ for 1000\[c{{m}^{2}}\], find the cost of cardboard required for supplying 250 boxes of each kind.

Answer 1

Hint: In the above question we will use the formula of total surface area of cuboid which is given as below;
\[\text{total surface area= }2(l\times b+b\times h+l\times h)\] where l=length, b= width and h= height.First we have to find total surface area of bigger dimension and add extra 5% of total surface area. Similarly calculate it for smaller dimension.Add total surface areas of both bigger and smaller dimension.Finally calculate cost required for total surface area by given data.

Complete step-by-step answer:

In the above question for the bigger box we have \[l=25cm,b=20cm\text{ and }h=5cm.\]
\[\begin{align}
  & \Rightarrow \text{total surface area =}2(25\times 20+20\times 5+25\times 5) \\
 & \Rightarrow \text{total surface area=}2(500+100+125) \\
 & \Rightarrow \text{total surface area =}1450c{{m}^{2}} \\
\end{align}\]
Also, extra area required for overlapping \[(1450\times \dfrac{5}{100})c{{m}^{2}}=72.5c{{m}^{2}}\].
While considering all over laps, total surface area of the bigger box = \[\begin{align}
  & (1450+72.5)c{{m}^{2}}=1522.5c{{m}^{2}} \\
 & \\
\end{align}\]
Area of cardboard sheet required for 250 such bigger boxes = \[(1522.5\times 250)c{{m}^{2}}=380625c{{m}^{2}}\].
Now, for the smaller boxes we have
\[\begin{align}
  & l=15,b=12\text{ and }h=5. \\
 & \Rightarrow \text{total surface area= }2(15\times 12+15\times 5+12\times 5)c{{m}^{2}} \\
 & \Rightarrow \text{total surface area=}2(180+75+60)c{{m}^{2}} \\
 & \Rightarrow \text{total surface area= }630c{{m}^{2}} \\
\end{align}\]
Also, the extra area required for overlapping $630\times \dfrac{5}{100}=31.5c{{m}^{2}}$
So, the total surface area of 1 smaller boxes while considering all overlapping
\[=(630+31.5)c{{m}^{2}}=661.5c{{m}^{2}}\]
Area of cardboard sheet required for 250 boxes =\[(250\times 661.5)c{{m}^{2}}=165375c{{m}^{2}}\]
Now, the total surface area of cardboard sheet required = (380625+ 165375)$c{{m}^{2}}$
=546000$c{{m}^{2}}$
Given, cost of 1000$c{{m}^{2}}$cardboard sheet = Rs. 4
Therefore, the cost of 546000$c{{m}^{2}}$cardboard sheet = Rs. \[(\dfrac{546000\times 4}{1000})=\text{ Rs}\text{.2184}\].
Therefore, the cost of cardboard required for supplying 250 boxes of each kind will be Rs. 2184.

Note: Be careful while doing calculation because there is a chance that you might make mistakes.
Also, remember the formula of total surface area of cuboid which i have already mentioned above.