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Question
CBSEENMA9003373
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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 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 र 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.

Solution

For bigger box
l = 25 cm b = 20 cm h = 5 cm
Total surface area of the bigger box
= 2 (lb + bh + hl)
= 2[(25)(20) + (20)(5) + (5)(25)]
= 2[500 + 100 + 125] = 1450 cm2
Cardboard required for all the overlap
equals 1450 cross times 5 over 100 equals 72.5 space cm squared

∴ Net surface area of the bigger box

= 1450 cm2 + 72.5 cm2 = 1522.5 cm2
∴ Net surface area of 250 bigger boxes
= 1522.5 x 250 = 380625 cm2
Cost of cardboard

equals 4 over 1000 cross times 380625 equals र space 1522.50

For smaller box

l = 15 cm b = 12 cm h = 5 cm
∴ Total surface area of the smaller box = 2 (lb + bh + hl)
= 2[(15)(12) + (12)(5) + (5)( 15)] = 2[ 180 + 60 + 75] = 630 cm2
Cardboard required for all the overlaps
equals 630 cross times 5 over 100 equals 31.5 space cm squared
∴ Net surface area of the smaller box
= 630 cm2 + 31.5 cm2 = 661.5 cm2 Net surface area of 250 smaller boxes = 661.5 x250 = 165375 cm2
∴ Cost of cardboard
equals 4 over 1000 cross times 165375 equals र space 661.50
Cost of cardboard required for supplying 250 boxes of each kind
= र 1522.50 + र 661.50 = र 2184.

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(i) Which box has the greater lateral surface area and by how much?

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(i) Which box has the greater lateral surface area and by how much?

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