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
25 cm x 20 cm x 5 cm and the smaller of dimensions 15 cm x 12 cm x 5 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 cm, find the cost of cardboard required for supplying 250 boxes of each
kind.​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer: -}}}}$

Dimension of bigger box = 25 cm × 20 cm × 5 cm

Total surface area of bigger box = 2(lb + bh + lh)

= 2(25×20 + 20×5 + 25×5) cm2

= 2(500 + 100 + 125) cm2

= 1450 cm2

Dimension of smaller box = 15 cm × 12 cm × 5 cm

Total surface area of smaller box = 2(lb + bh + lh)

= 2(15×12 + 12×5 + 15×5) cm2

= 2(180 + 60 + 75) cm2

= 630 cm2

Total surface area of 250 boxes of each type = 250(1450 + 630) cm2

= 250×2080 cm2 = 520000 cm2

Extra area required = 5/100(1450 + 630) × 250 cm2 = 26000 cm2

Total Cardboard required = 520000 + 26000 cm2 = 546000 cm2

Total cost of cardboard sheet = ₹ (546000 × 4)/1000 = ₹ 2184.

Answer 2

$\pmb{ \sf{Question :}}$

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 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 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 cm², find the cost of cardboard required for supplying 300 boxes of each kind.

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$\pmb{ \sf { Formula \: to \: be \: used: }}$

$:\mapsto{\small{\underline{\boxed{\sf{TSA \: of \: cuboid =2(lb +bh + hl)}}}}}$

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$\pmb{\sf{Solution : }}$

$\red \bigstar\textsf{ \: For bigger box,}$

$\textsf{ l= 25 cm b = 20 cm h = 5 cm}$

$\textsf{Total surface area of the bigger box} \\ \textsf{= 2 (lb + bh + hl)} \\ \textsf{= 2[(25)(20) + (20)(5) + (5)(25)]} \\ \textsf{= 2(500 + 100 + 125) = 1450 cm²}$

$\sf{Cardboard \: required \: for \: all \: the \: overlap }\\ \sf{ = 1450 \times \frac{5}{100} = 72.5 \: {cm}^{2} }$

$\sf{\therefore Net \: surface \: area \: of \: the \: bigger \: box} \\ \sf{= 1450 cm² + 72.5 cm² = 1522.5 cm²}$

$\therefore \textsf {Net surface area of 250 bigger boxes} \\ \sf{= 1522.5 \times 250 = 380625 cm²}$

$\sf{Cost \: of \: cardboard = \frac{4}{1000} \times 38065 = ₹1522.50}$

$\red \bigstar \textsf { \: For smaller box,}$

$\textsf{I = 15 cm b = 12 cm h = 5 cm}$

$\textsf{Total surface area of the smaller box} \\\textsf{= 2 (lb + bh + hl)} \\\textsf{= 2[(15)(12) + (12)(5) + (5)( 15)] }\\\textsf{= 2[ 180 + 60 + 75] }\textsf{= 630cm²}$

$\textsf{Cardboard required for all the overlaps} \\ \sf{ = 630 \times \frac{5}{100} = 31.5 {cm}^{2} }$

$\therefore \textsf{Net surface area of the smaller box} \\\sf{= 630 cm^2 + 31.5 cm^2 = 661.5 cm^2}$

$\therefore \textsf{Net surface area of 250 smaller boxes} \\ \sf{ = 661.5 \times 250 = 165375 cm^2}$

$\sf{Cost \: of \: cardboard = \frac{4}{1000} \times 165375 = ₹661.50}$

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$\pmb{\sf{Final \: Answer :}}$

$\textsf{Total Cost = ₹ 1522.50 + ₹661.50} \\ = \boxed{ \underline{\large{\sf \pink{ ₹2184}} }}$

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$\pmb{ \sf{Note : }}$

$\footnotesize \rm{ : \mapsto For \: diagrams, \: refer \: to \: the \: attachment}$

$\footnotesize \textrm{:↦ Do thanks and rate the answer if it was helpful}$