# 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 = 6a^{2} (where, 'a' is the side of the cube)

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

Lateral surface area of a cube = 4a^{2}

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 = 4a^{2}

= 4 × (10 cm)^{2}

= 4 × 100 cm^{2}

= 400 cm^{2}

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

= 2 × (12.5 cm + 10 cm) × 8 cm

= 2 × 22.5 cm × 8 cm

= 360 cm^{2}

We see that, the cubical box has a greater lateral surface area by (400 cm^{2} - 360 cm^{2}) = 40 cm^{2}

Total surface area of the cube = 6a^{2}

= 6 × (10 cm)^{2}

= 6 × 100 cm^{2}

= 600 cm^{2}

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 cm^{2} + 80 cm^{2} + 100 cm^{2})

= 2 × 305 cm^{2}

= 610 cm^{2}

Cubical box has a smaller total surface area by (610 cm^{2} - 600 cm^{2}) = 10 cm^{2}

Thus, the cubical box has a greater lateral surface area by 40 cm^{2} and the cubical box has a smaller total surface area by 10 cm^{2}.

**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 cm^{2} and the cubical box has a smaller total surface area by 10 cm^{2}.