# 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.

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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 $546000\ cm^2 = Rs.\ \frac{4}{1000}\times546000$

$= Rs.\ 2184$

Updated on 10-Oct-2022 13:42:09