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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 $ 25 \mathrm{~cm} \times 20 \mathrm{~cm} \times 5 \mathrm{~cm} $ and the smaller of dimensions $ 15 \mathrm{~cm} \times 12 \mathrm{~cm} \times 5 \mathrm{~cm} $. For all the overlaps, $ 5 \% $ of the total surface area is required extra. If the cost of the cardboard is $ Rs.\ 4 $ for $ 1000 \mathrm{~cm}^{2} $, find the cost of cardboard required for supplying 250 boxes of each kind.
Given:
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 \( 25 \mathrm{~cm} \times 20 \mathrm{~cm} \times 5 \mathrm{~cm} \) and the smaller of dimensions \( 15 \mathrm{~cm} \times 12 \mathrm{~cm} \times 5 \mathrm{~cm} \).
For all the overlaps, \( 5 \% \) of the total surface area is required extra.
The cost of the cardboard is \( Rs.\ 4 \) for \( 1000 \mathrm{~cm}^{2} \)
To do:
We have to find the cost of cardboard required for supplying 250 boxes of each kind.
Solution:
Length of a bigger box $l = 25\ cm$
Breadth of a bigger box $b = 20\ cm$
Height of a bigger box $h = 5\ cm$
This implies,
The total surface area of a bigger size box $=2 ( lb + bh + lh)$
$= 2(25 \times 20 + 20 \times 5 + 25 \times 5)$
$= 2(500+ 100+ 125)$
$= 2(725)$
$= 1450\ cm^2$
Length of a smaller box $l = 15\ cm$
Breadth of a smaller box $b = 12\ cm$
Height of a smaller box $h = 5\ cm$
This implies,
The total surface area of a smaller size box $=2 ( lb + bh + lh)$
$= 2(15 \times 12 + 12 \times 5 + 15 \times 5)$
$= 2(180+ 60+ 75)$
$= 2(315)$
$= 630\ cm^2$
Extra total surface area required for a bigger box $=5 \%$ of $1450\ cm^2$
$=\frac{5}{100}\times1450$
$=72.5\ cm^2$
Extra total surface area required for a smaller box $=5 \%$ of $630\ cm^2$
$=\frac{5}{100}\times630$
$=31.5\ cm^2$
The total surface area of a bigger box and overlap $=(1450+72.5)\ cm^2$
$=1522.5\ cm^2$
The total surface area of 250 bigger boxes and overlaps $=250\times1522.5\ cm^2$
$=380625\ cm^2$
The total surface area of a smaller box and overlap $=(630+31.5)\ cm^2$
$=661.5\ cm^2$
The total surface area of 250 smaller boxes and overlaps $=250\times661.5\ cm^2$
$=165375\ cm^2$
Total cardboard required $=380625+165375$
$=546000\ cm^2$
Cost of the cardboard for $1000\ cm^2 = Rs.\ 4$
Cost of the cardboard for $1\ cm^2 = Rs.\ \frac{4}{1000}$
Cost of the cardboard for $546000\ cm^2 = Rs.\ \frac{4}{1000}\times546000$
$= Rs.\ 2184$
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