NCERT Solutions for Class 9 Maths Chapter 13

Important NCERT Questions

Surface Areas and Volumes

NCERT Books for Session 2022-2023

CBSE Board, UP Board and Other state Boards

EXERCISE 13.1

Page No:213

Questions No: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 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 250 boxes of each kind.

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For smaller boxes:

Length of box l = 25 cm, breadth b = 20 cm and height h = 5 cm

Total surface area of 1 bigger box = 2(lb + bh + hl)

= 2(25 × 20 + 20 × 5 + 5 × 25) cm² = 2(500 + 100 + 125) cm² = 2(725) cm² = 1450 cm²

Area of cardboard for overlap = 5% of 1450 cm² = 1450 × (5/100 = 72.5 cm²

Total area of cardboard for 1 bigger box = 1450 + 72.5 = 1522.5 cm²

Therefore, the area of cardboard for 250 bigger boxes = 250 × 1522.5 cm² = 380625 cm²

For smaller boxes:

Length of box l = 15 cm, breadth b = 12 cm and height h = 5 cm

Total surface area of 1 smaller box = 2(lb + bh + hl)

= 2(15 × 12 + 12 × 5 + 5 × 15) cm² = 2(180 + 60 + 75) cm²

= 2(315) cm²

= 630 cm²

Area of cardboard for overlap = 5% of 630 cm² = 630 × (5/100) = 31.5 cm²

Total area of cardboard for 1 smaller box = 630 + 31.5 = 661.5 cm²

Therefore, the area of cardboard for 250 smaller boxes = 250 × 661.5 cm² = 165375 cm²

So, the area of cardboard for 500 boxes = 380625 + 165375 = 546000 cm²

Total cost of cardboard at the rate of Rs 4 per 1000 cm² = Rs 546000 × 4/1000 = Rs 2184

Hence, the total cost of cardboard for 500 boxes is Rs 2184.