Question

Question 7
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 area is required extra. If the cost of the cardboard is $Rs.4for1000c{m}^2$, find the cost of cardboard required for supplying 250 boxes of each kind.

Answer 1

Length $\left(l_1\right)$ of bigger box = 25 cm
Breadth $\left(b_1\right)$ of bigger box = 20 cm
Height $\left(h_1\right)$ of bigger box = 5 cm
Total surface area of bigger box = 2(lb + lh + bh)
$=\left[2\right(25\times 20+25\times 5+20\times 5\left)\right]c{m}^2$
$=\left[2\right(500+125+100\left)\right]c{m}^2$
$=1450c{m}^2$
Extra area required for overlapping$=\left(\frac{1450\times 5}{100}\right)c{m}^2$

$=72.5c{m}^2$
While considering all over laps, total surface area of 1 bigger box
$=(1450+72.5)c{m}^2=1522.5c{m}^2$
Area of cardboard sheet required for 250 such bigger boxes
$=(1522.5\times 250)c{m}^2=380625c{m}^2$
Similarly, total surface area of smaller box $=\left[2\right(15\times 12+15\times 5+12\times 5]c{m}^2$
$=\left[2\right(180+75+60\left)\right]c{m}^2$
$=(2\times 315)c{m}^2$
$=630c{m}^2$
Therefore, extra area required for overlapping$=\left(\frac{630\times 5}{100}\right)c{m}^2=31.5c{m}^2$

Total surface area of 1 smaller box while considering all overlaps
$=(630+31.5)c{m}^2=661.5c{m}^2$
Area of cardboard sheet required for 250 smaller boxes $=(250\times 661.5)c{m}^2$
$=165375c{m}^2$
Total cardboard sheet required $=(380625+165375)c{m}^2=546000c{m}^2$
Cost of $1000c{m}^2$ cardboard sheet = Rs. 4
Cost of 546000 cm² cardboard sheet
$=Rs.\left(\frac{546000\times 4}{1000}\right)=Rs.2184$
Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be Rs. 2184.