Surface Areas & Volumes | Exercise 13.1 | Q5

Question 5: A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i)  Which box has greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?

Explanatory Answer | Exercise 13.1 Question 5

Given Data

Dimensions of cubical box: Each edge is 10 cm
Dimensions of cuboidal box: Length 12.5 cm, width 10 cm and height 8 cm

Part (i): Lateral surface area

Lateral surface area of cubical box = 4a², where ‘a’ is the edge of the box
= 4 × 10² = 400 cm²
Lateral surface area of cuboidal box = 2h (l + b)
= 2 × 8 (12.5 + 10)
= 360 cm²
The cubical box has greater lateral surface area. It has 40 cm² more area.

Part (ii) : Total surface area

Total surface area of cubical box = 6a², where ‘a’ is the edge of the cubical box.
= 6 × 10²
= 600 cm²
Total surface area of cuboidal box = 2 (lb + lh + bh)
= 2 (12.5 × 10 + 12.5 × 8 + 8 × 10)
= 610 cm ²
The cubical box has smaller total surface area. It is lesser by 10 cm²

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 ▶