Surface Areas & Volumes | Exercise 13.1 | Q7

CBSE Class 9 Maths | NCERT Solution to Exercise | Surface Area of a Cuboid

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


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Explanatory Answer | Exercise 13.1 Question 7

Step 1: Compute Area of the Cardboard Boxes

Dimensions of bigger box = 25 cm × 20 cm × 5 cm
Area of cardboard required for 1 big box = Total surface area of cuboid
= 2 (lb + lh + bh)
= 2 (25 × 20 + 25 × 5 + 20 × 5)
Area of cardboard required for 1 big box = 1450 cm2

Dimensions of smaller box = 15 cm × 12 cm × 5 cm
Area of cardboard required for 1 small box = Total surface area of cuboid
= 2 (lb + lh + bh)
= 2 (15 × 12 + 15 × 5 + 12 × 5)
Area of cardboard required for 1 small box = 630 cm2

Step 2: Compute Overlapping Areas of Cardboard Boxes

Area required for overlaps of 1 big box = 5% of 1450
= \\frac{5}{100}) × 1450 = \\frac{1}{20}) × 1450 = 72.5 cm2
Area required for overlaps of 1 small box = 5% of 630
= \\frac{5}{100}) × 630 = \\frac{1}{20}) × 630
= 31.5 cm2

Step 3: Compute Total Cost of Cardboard

Area of cardboard required for 250 boxes of each size
= (1450 + 72.5 + 630 + 31.5 ) × 250 cm2
= (2174) × 250 cm2

Cost of cardboard = Rs.4 for 1000 cm2
i.e., Rs. \\frac{4}{1000}) per cm2
Total cost of cardboard = Area of cardboard required for 250 boxes of each time × cost per cm2
\\frac{2174 × 250 × 4} {1000})
= Rs. 2174

Note: Avoid computing the result at the end of each step. It saves you time on two counts.
1. If you leave the calculation for the last step, you save time on not calculating at each intermediate step.
2. As you may have noticed in the calculation for this question, many numbers may cancel each other at the last step. So, it makes calculations easier.

 


NCERT Solutions for Class 9 Math | Chapter 13 Video Solutions



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