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

Solution:

Since the cardboard boxes are cuboidal in shape, the total area of the cardboard is the same as the total surface area of the cuboid added to the overlap area that is, 5% of the total surface area is required extra.

Hence, the area of each box can be obtained by adding 5% of the total surface area to the total surface area of the cuboid.

Total surface area of cuboid = 2(lb + bh + hl)

For bigger box:

Let the length, breadth and height of the bigger box be L, B and H respectively.

Length, L = 25 cm

Breadth, B = 20 cm

Height, H = 5 cm

The area of the card board = 2(LB + BH + HL)

= 2 × (25cm × 20cm + 20cm × 5cm + 5cm × 25cm)

= 2 × (500cm² + 100cm² + 125cm²)

= 2 × 725 cm²

= 1450 cm²

For all the overlaps, 5% of the total surface area is required extra. Therefore,

Overlap area = 5% of 1450 cm²

= 5/100 × 1450cm²

= 72.5 cm²

Net area of the card board required for each bigger box = 1450 cm² + 72.5 cm² = 1522.5 cm²

We can now find the area of  250 such boxes and the total cost of the cardboard at ₹4 per 1000 cm^².

Area of card board required for 250 such boxes = 250 × 1522.5 cm² = 380625 cm²

The total cost of the cardboard at ₹4 per 1000 cm² = (4/1000) × 380625 = ₹1522.50

For smaller box:

Let the length, breadth and height of the smaller box be l, b and h respectively.

Length, l = 15 cm

Breadth, b = 12 cm

Height, h = 5 cm

The area of the cardboard = 2(lb + bh + hl)

= 2 × (15 cm × 12 cm + 12 cm × 5 cm + 5 cm × 15 cm)

= 2 × (180 cm² + 60 cm² + 75 cm²)

= 2 × 315 cm²

= 630 cm²

For all the overlaps, 5% of the total surface area is required extra. Therefore,

Overlap area = 5% of 630cm² = (5/100) × 630 cm² = 31.5 cm²

Net area of the cardboard required for smaller box = 630 cm² + 31.5 cm² = 661.5 cm²

Area of cardboard required for 250 such boxes = 250 × 661.5 cm² =165375 cm²

The total cost of the cardboard at ₹4 per 1000 cm² = ₹ (4/1000) × 165375 = ₹661.50

Cost of cardboard required for supplying 250 boxes of each kind = ₹1522.50 + ₹661.50 = ₹2184

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

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Video Solution:

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

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.1 Question 7

Summary:

It is 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 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. We have found that the cost of cardboard required for supplying 250 boxes of each kind is ₹2184.

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