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 the greater lateral surface area and by how much?
ii) Which box has the smaller total surface area and by how much?

Solution:

Given: The length of the edge of the cubical box is 10cm and the length, breadth, and height of the cuboidal box are 12.5 cm, 10 cm, and 8 cm respectively.

A cube is a cuboid whose length, breadth, and height and equal. A cuboid has six faces and the total surface area is the sum of the surface area of the 6 faces and the Lateral surface area is the sum of the area of the four faces.

Total surface area of cube = 6a² (where, 'a' is the side of the cube)

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

Lateral surface area of a cube = 4a²

Lateral surface area of cuboid = 2(l + b)h

Edge length of the cube, a = 10 cm

Length of the cuboid, l = 12.5 cm

Breadth of the cuboid, b = 10 cm

Height of the cuboid, h = 8 cm

Lateral surface area of the cube = 4a²

= 4 × (10 cm)²

= 4 × 100 cm²

= 400 cm²

Lateral surface area of the cuboid = (l + b)h

= 2 × (12.5 cm + 10 cm) × 8 cm

= 2 × 22.5 cm × 8 cm

= 360 cm²

We see that, the cubical box has a greater lateral surface area by (400 cm² - 360 cm²) = 40 cm²

Total surface area of the cube = 6a²

= 6 × (10 cm)²

= 6 × 100 cm²

= 600 cm²

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

2(lb + bh + hl) = 2 × (12.5 cm × 10 cm + 10 cm × 8 cm + 8 cm × 12.5 cm)

= 2 × (125 cm² + 80 cm² + 100 cm²)

= 2 × 305 cm²

= 610 cm²

Cubical box has a smaller total surface area by (610 cm² - 600 cm²) = 10 cm²

Thus, the cubical box has a greater lateral surface area by 40 cm² and the cubical box has a smaller total surface area by 10 cm².

☛ Check: Class 9 Maths NCERT Solutions Chapter 13

---

Video Solution:

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 the greater lateral surface area and by how much? ii) Which box has the smaller total surface area and by how much?

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.1 Question 5

Summary:

It is given that there is a cubical box that has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. We have found that the cubical box has a greater lateral surface area by 40 cm² and the cubical box has a smaller total surface area by 10 cm².

---

☛ Related Questions:

• A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine:i) The area of the sheet required for making the box.ii) The cost of sheet for it, if a sheet measuring 1m² costs ₹ 20.
• The length, breadth and height of a room are 5 m, 4 m, and 3 m respectively. Find the cost of white washing the walls of the room and ceiling at the rate of ₹7.50 per m2.
• The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15000, find the height of the hall.[Hint: Area of the four walls = Lateral surface area.]
• The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?