Surface Areas & Volumes | Exercise 13.1 | Q7

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.

Video Explanation

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.

Exercise 13.1 | Surface Area of Cubes & Cuboids

1. Class 9 Exercise 13.1 Question 3 | Height of hall ▶
2. Class 9 Exercise 13.1 Question 6 | TSA of Herbarium ▶
3. Class 9 Exercise 13.1 Question 7 | Shanti Sweets ▶

Exercise 13.2 | Surface Area of Cylinders

1. Class 9 Exercise 13.2 Question 3 | CSA TSA of Metal Pipe ▶
2. Class 9 Exercise 13.2 Question 4 | Roller & Playground ▶
3. Class 9 Exercise 13.2 Question 9 | Cylindrical Petrol Tank ▶
4. Class 9 Exercise 13.2 Question 10 | CSA of Decorative Lampshade ▶

Exercise 13.3 | Surface Area of Cones

1. Class 9 Exercise 13.3 Question 5 | Length of Tarpaulin 3 m wide ▶
2. Class 9 Exercise 13.3 Question 8 | Cost of painting conical barricades ▶

Exercise 13.4 | Surface Area of Spheres & Hemispheres

1. Class 9 Exercise 13.4 Question 8 | Outer CSA of hemispherical bowl ▶
2. Class 9 Exercise 13.4 Question 9 | Surface area of sphere & Cylinder ▶